{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analyze Big Financial Data**\n",
    "\n",
    "O'Reilly (2014)\n",
    "\n",
    "Yves Hilpisch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mathematical Tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['font.family'] = 'serif'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "uuid": "460b709e-eed1-48e4-b3ad-d07377ea5de6"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "uuid": "2326c3ad-f244-4f48-8b68-851bd2347d57"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "uuid": "c09f73d2-c2a5-4c6d-a2f1-08a191378417"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true,
    "uuid": "96d2bd1b-8883-486d-920d-b610aeb076a8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'f(x)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b')\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot\n",
    "# title: Example function plot\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Monomials as Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "uuid": "ace90420-7219-4227-8210-bf107f556726"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=1)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "uuid": "c0667d3e-a48a-413d-b250-5e0d3b58275e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'f(x)')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_1\n",
    "# title: Example function and linear regression\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "uuid": "096bb07a-55f7-45de-8734-2a76d8749d53"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=5)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "uuid": "5e17309e-e8e2-4df9-b841-0f57d983b89e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'f(x)')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_2\n",
    "# title: Regression with monomials up to order 5\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "uuid": "67b14a21-e8f2-4dd4-a43b-0d232f2b4055"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), 7)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "uuid": "053752b7-7eb3-4d93-acdf-69874ceada12"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'f(x)')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_3\n",
    "# title: Regression with monomials up to order 7\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "uuid": "e600b6be-4cf2-4212-807a-7f397f081e98"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "uuid": "bc6918fe-f520-483c-94eb-41dd89abfa70"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0017769134759517435"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((f(x) - ry) ** 2) / len(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Individual Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "b4f05890-56e0-4f29-9d61-bd9948ad8af0"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((3 + 1, len(x)))\n",
    "matrix[3, :] = x ** 3\n",
    "matrix[2, :] = x ** 2\n",
    "matrix[1, :] = x\n",
    "matrix[0, :] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "uuid": "c8963eee-4bc8-4ef2-a172-d4b64fd065a3"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-15-6c763b92a05e>:1: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  reg = np.linalg.lstsq(matrix.T, f(x))[0]\n"
     ]
    }
   ],
   "source": [
    "reg = np.linalg.lstsq(matrix.T, f(x))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "efd077d1-9c8a-4961-be95-400f83cd679e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.13340410e-14,  5.62777448e-01, -8.88178420e-16, -5.43553615e-03])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "efb7b252-d0f8-4263-b2be-4d9588ab06a7"
   },
   "outputs": [],
   "source": [
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "1b1953fe-83a2-436b-8cd4-69c5abf6d2e1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'f(x)')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_4\n",
    "# title: Regression via least-squares function\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "ac77ef01-8abe-4b99-8f92-8325a396ff2c"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-33-227fdb1d4114>:2: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  reg = np.linalg.lstsq(matrix.T, f(x))[0]\n"
     ]
    }
   ],
   "source": [
    "matrix[3, :] = np.sin(x)\n",
    "reg = np.linalg.lstsq(matrix.T, f(x))[0]\n",
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true,
    "uuid": "58d9db31-5885-4fba-8ae7-2e962a0963ca"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'f(x)')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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R63DAtU/EUXSBN9FoawJD37yEXr0iSUqqvnU9a9ZY+cerl6CtgbVdZGXJnIAQ1cT2jXnUvTaR14pTeDwigawFS2gYF+U9WHr37jMOB8cWeecRSuq0pv/rdmbPtnLzzZHccFUm42/fRL3EhGozV7Brl4WBAyPIKraw9f0k6tXfatq5EOkJCFENbN9uZdytacQXe4dkmuWncF72b/4NojTR1D0/iqlTC/nxxzx6djzGxB+7ceH9vaBTIu5jTv/G5ANZWXDXXREcPmxl4sRCrrg2wptgTZgAQJKAEKaXlmahf/8Ilh9rw+FYBQTG0ESbNiXMG7eBVngTU+wRzcg+O9myxbwfO0VFMGhQBKmpITzwgIv77gvMPQIqw7zvhhCCnTst3HhjJOnpVp4eb8OzeonPxv7PRnFCK9xx3rmCfTUUX//elt69Ixk3zk5ensHBVZLHA08+GcbPP9u45poixowJvK0iz4YkASFMas8eCwMGRHLggJUxYwoYPLjoxNh/ACQAoKzmIHPBYuybljDzMyuNG3uYPj2Ma6/wsO39DeA0xxDRu9MKSZ29kc6ts3jjjQJCqsmctyQBIUxof2ou4/r+SubePEaPLmTIkAAeljgpMfXoUUxSUi6P3H+Uz/d0oedTPXG1T+TonsBdQd7jgRmTXdz44uWspitJ+Z1xYI7EVRGSBIQwmcO7conqmcjX6d1Iq9ORhwcdNTqkSomKgudv2lQ2V9A4WzO8107mzLERaLWrLhc8/HA4C6buKIs3fGeqKesByiNJQAgTKS6Gaf/3Oxe4vR9I9Y6Ys0DJrU7MFWTUVWwquohHHonghhsiSE0NjI+lzEy49dYI5s4NxdY2gYLmVVhwF0AC468thKiQqVPtfLS5HXuiAucpoLNy0lwBa5aw8BcL11xTxMqVNhITI3llnIui5WsNmy/YudPCtddG8csvNvr2LeLj+VZyFvuu4M5IkgSEMImlS0OYOtVOnaaRuJYH1lNAZ+WkuYImTTzMmlXABx/kc37dHO6Z3p1G/a/E0iUR11H/JoJ1S/MZffWvHPw9j6FDXbz3XgGRkQTepHsVkSQghAkcOGBhyJBwbDZ45518ajaunh9Iffq4WTpjXdn4e90MzYOX72L27FCKfDz3nZkJk5910fyWHizK7sbueh15/vEjWKv5p2Q1b54Q5ud2w+DB4Rw+bGXcuEIuvrjcHVirhdD2J+YLDtZSrMy+iBEjwunePYqvZhdgXVu1w0ROJ7zyip2OHR38/PYOEkoTUJ1D5pxvqSxJAkIEuBdftLN6tY3rry9i0KAAfhS0qpw0XxCyYQlL11kYNMhF5h+5dB9xBXX6XknRxYms+Smf4uKzvIbTScnKtfzn9UI6d45i0qQw7HYPN45qWbYQnmnnWypJ9hMg8NaBPxtmb4PZ4wcftMHpZMOHqQx4vgP1mkfy44+5REdX3en/KtDfgyPfryNhYK+y77uwit31O9Gvn5sbrz5GF8dW6lzRmYz8kz4mTtoPuTjCwY4dVn5bk0e/Fy6n4THvxjiJUWu4d6idBx5wef++Bu6hHJQbzQshTsHpJLpXT3rvSmWdJYH015cSHR1pdFSGqnNFAu4477aX2Y0VbbrHsX2RhTnvuhjxbg/qkML2kATujF9FdMMomtTKYfKSRGIzNbvCE+hsWUNGfhSd2cpgvHsAtCKFVe+tI6pXxxMX8vWKqwFGkoAQASgkJZnwXakAJHhSqB+yDTfB88F0Sn/Z9vJFRyjjipxse38DrZ71juPHFacQkZbMT8ld6UwqDUo/7M8vSKHX+b9Cl050atUS53vxOP5IxR0XT1TnBCNbZThJAkIEoHkpbehOAq1ICZqx6Qr5y116aCi0vzMe9yxvD4GEBD7/vhlOcjiyuxnOu+Nx7E3F1TKe139oDo4CIIz8e5ZSZNCQT6CRJCBEgDl6FJ6eUAdrxBqS3lhH3R7VZzMWnziphxDTvTPke3AAjgujyF9Wzod9kA35nI48HSREgBk7NpwjR6wMfTKUun07SgKoiPIKuappgVdVkiQgRAD5+ecQ5swJpU2bYu/S0EL4mKHDQUqpBsB4oJ3WWvpmIqjl58PIkeFYrR5eeaUAmwzWCj8wuifQHfgaKPcZViGCxbRpdnbutDJ4cBHt2lXvqmAROAxNAlrrz4HArU4Rwk+Sk628/rqd884r4Z//rB7bFgpzMFWHMyYmEpvNN3u6xcb6sBTTT8zeBrPHD2fXhpJsJx8M2UqY+0LeestB8+bG/R2C9T0IJP6O31RJIDPTNztTB3q5fEWYvQ1mjx/Osg1OJ9YuibyXoRnrUIS1WkJGhjFPsgTtexBAfLhsRLnHjJ4TECKo5a9Lpk6Gt6q1iTM4Vq0UgcXQJKCU6gHcDTRUSo1WSkUYGY8Q/jb1v+1JxrtsgVQGCyMYOhyktU4CkoyMQQijpKVZePPDGH44bzVLZ6zDcpEsYSD8z1RzAkJUJ+PGhVFUZGHkmFAsXaVMRhhD5gSEMMCKFSF8/30oXbq4ue46t9HhiCAmSUAIPyspgeeeCwNg3LhCLFIqKQwkSUAIP/v0UxtbtoRw001F1X6/YBH4JAkI4Ue5uTBxYhjh4R5GjZLKYGE8SQJC+NEbb9g5eNDKkCEuGjc2z/7eovqSJCCEn6T/nsvq1zZyft1shg1zGR2OEIAkASH8w+kkpndPkgovZZ21Mw6cRkckBCBJQAi/2LdI0zjbuzxEnUOyPIQIHJIEhPCDcfPayfIQIiBJxbAQPrZhg5Uvf4jh8MWr+GrCeooTZHkIETgkCQjhYxMmeAvDHn8+lOKOsjyECCwyHCSEDy1bFsLPP9tITHTTrVux0eEI8T8kCQjhIx6PtzAM4JlnpDBMBCZJAkL4yIIFNjZsCKFfP9k4XgQuSQJC+EBxMUyaZMdq9fDUU1IYJgKXJAEhfGDePBspKSHcequbuDjpBYjAJUlAiCrmcsGUKWHY7R5GjpS5ABHY5BFRIarY3PcKabDnN64fGMd554UaHY4Qp1WhJKCUCgdaALHAMWCn1jrbl4EJYUb5GU6uG9eLEaRQuCyebOdSKQwTAe20w0FKqRil1H+AQ8By4EPgR+CAUuo7pVS8H2IUwjQWvrKd+OIUAMLSUmWNIBHwyk0CSqkawGzga6Cx1rq21rqp1joWiAEmAy8ppVr7J1QhAltODrzwRXu0VdYIEuZxuuGgpsA9Wusjfz2gtXYBy5RSK4AuvgpOCDP517/gj8wafDxiOY9evdmbAGQoSAS4cpOA1nrr8a+VUm211ltOPq6UGqC1ngf8ci4BKKWuAvrjHXLyaK3Hnsv5hDDCsWPw8stQu3YJA4fZcTtkjSBhDhV9RPQ1pVT08W+UUp2ASed6caVUJPAW8JjWegzQVil15bmeVwh/e+stO1lZMGyYS27+halU9BHR7cA0pdRc4DJgILC/Cq5/KbBba338YepfgL7A4io4txB+ceSIhbfftlO/PgwaVGR0OEJUSkWTwHN4Hw9dhvcR0Q5QJfvj1QNyTvo+u/S1U4qJicRmC6mCy/6v2NjoM/9QgDN7G8wa/0svQW4uTJwIzZqZsw3HmfU9OJnZ2+Dv+CuaBJYCUcCDgAamAGHAned4/UPAyS2uUfraKWVm5p3j5U4tNjaajIycM/9gADN7G8waf3q6henTo2jUyMPgwVZTtuE4s74HJzN7G3wV/+kSS0XnBLKAjlrrT7TWG4EhQN0qiG0l0EwpFVb6/WXAd1VwXiH84rXX7OTnWxgxwkV4uNHRCFF5FU0CQ7TWB49/o7UuAIae68W11nnAQ3gnnscDW7TWMh8gTGHfPgsffBBK06Yl3H67zAUIcyp3OEgp1Q3vI5srtdbr/npca71DKdUY6Ka1/uxsA9Ba/wD8cLa/L4RRZkx20d61jfuGtyA0VLoBwpxOVyewQik1Syl1D94P6T1ALhAONAC6A52BAf4IVIhAsue3XEZ8kkgrUnC/HU/mgKVg8glJEZzONDGci3fc/v+AtnjnAbLwPjL6GXDdSY93ChE05o37nYl41wiy7ShdI6h5Q4OjEqLyzjQnUKC1ngVs01o31lqHaa3raa0vAw5JAhDBKDnZyus/tSXNLmsECfM7U09AKaUG4a3kvecvx+4CPvZNWEIErkmT7DgJZd2bScQ02iprBAlTO1MSmAjcAzQBEv9yrLFPIhIigK1fb2XBglA6d3bT87oI3BZZI0iY22mTgNZ6ObBcKdVfa/3FyceUUv19GpkQAWjiRG9Jy6hRLiwWg4MRogpUqE7grwmgvNeEqM6WLQvh559t9Orl5tJLi40OR4gqIRvNC1EBHs+JXsAzz8jzEKL6kCQgRAUsWGBjw4YQrr++iLZtS4wOR4gqI0lAiDMoLoYXX7RjtXp48kmX0eEIUaUkCQhxBvPm2dA6hNtuKyIuTnoBonqRJCDEaRRlOln0wiZiQnMYOVJ6AaL6qeh+AkIEH6cTe/dEvs7QHKilsNVaAkhRmKhepCcgRDkK1idTN0MD0PCY9q4PJEQ1I0lAiHK8uqg9ycj6QKJ6k+EgIU5h1y4LMz6I4fvGq0l6Yx3WNrI+kKieJAkIcQrjx4fhclkY8Vwo1ktlfSBRfclwkBB/sXp1CPPnh9KhQzE33OA2OhwhfEqSgBAnKSmB55/3Lg8xblyBLBInqj1JAkKc5MsvvctD3HBDEZ06SWGYqP4kCQhRKj/fOxcQFuZh9GhZJE4EB0kCQpT697/t7NtnZfBgF02beowORwi/kCQgBHB4Vy7Lp26kWZ1sHnlElocQwUOSgBBOJzWu6snSgktZH9KZGlan0REJ4TeGJQGllFUp9YBS6pBS6iKj4hAiZV4qjbO9y0PUOSTLQ4jgYmRPoB2wGsgzMAYR5AoLYfhbsjyECF6GVQxrrTcCKKWMCkEIXnvNzubfw5h+zy+Mv32TNwHI8hAiiFg8Ht89BaGUWgjUP8Wh57TW80t/ZhdwndZ665nO53YXe2y2kCqNUQSv5GRo3x5iY+G336BGDaMjEsJnyi179GlPQGvduyrPl5npm5Gj2NhoMjJyfHJufzF7G/wdf0kJDBoUgctlY+LEfAoL3WRknNs55T0wntnb4Kv4Y2Ojyz0mTweJoPTRR6GsWmWjb98i+vSR9YFE8DLy6aAYpdRooCYwWCnV1ahYRHBJT7cwdmwY0dEeJk6UymAR3IycGM4Expf+J4TfjB4dRna2hcmTC2jYUCqDRXCT4SATKTziJPuHdRRn/aWYyemE1au9/ytO66f5+Rz4egNXXJLFvfcWGR2OEIaTTWUCkdOJZ2sy27iQ9bomW7ZY0evzmflbL1qRQjIJXFN7NVH1ozgvJof3fk2EHE14E0V+0hIs0fKI46lk/uHkkgd7sZoU8g7Hk5u3VB4HFUFPegIBZsOyPPIu6kW966+kwfU9GfOEmw8/tBO2I5lWpADQihQ6RW1l/34rx1ZomuR4q12j92oGddnFs8+GsW6dFY8HcDqxrV8b9L2EkhJ4/cE04tzev2HknlSpDBYCSQIB47ffrNx9dwTP3bSLZnknPuzffXQ9S5bkMndrM9xx8YC3qvXNpOZs3+7ki5SmFDT3vr6vhmKj6yLeftvOtddGcfnFHoovSSSmz5XE9O4Z1Ilg+nQ7/1nbjt2RUhksxMlkOMhITifpP6Xw4vz2zPmmFh6PhZ4dFTkHFdF7Ne64eK58OB4cJYCDzIVLsenkP1W12ms7yFm8lPBDe7DXa8oaOyxblsdXX4WS8e1vNMjz9hJs21M59ksKtXp3NLDBxli5MoQXX7RTr2Eo+fOXkHn4N6kMFqKUTyuGq1pGRo5PgjWiwCQ/w4mtWyKNsjTJJHBvq1WMeC6UXr2KseQ6/+fD/kxO1QbXUSeRPROJOei9xuVha7j5vjCGD3cRGxtY77uv3oOMDAu9ekVy+LCFL7/Mp2vX4iq/xnFSqGQ8s7fBh8Vi5VYMy3CQAQ4dsvBs/500yvLepbcihQVT13PllcXePW0dDtwdOp3znaq9tgP3iiUc/nYxS6csI7JeFG+9ZadTpyheHuOiIKl6zxUUF8NDD4WTnm7lmWdcPk0AQpiVJAE/S0mx0qdPJPN0W/ZFexfPc8fFU5Lgo/FphwNP507cNDCcFStyefHFArXAt/cAAA6ASURBVOpF5jDwje6cd/OV2LolVttE8MordpYts/G3v7kZOlQ2ihHiVCQJ+NHSpSH07RvJH39YGfZkKPbNS8hcsJjMhUv9Mj4dFgb331/EinfWlT1pFHNQ89yANNLSyu0tmtIvC/NZ9tJG4htl8/rr+VjlX7oQpyT/1/CTDz8M5fbbIygshLfeyufxx11VNuxTWbZ2rcqeNNodmcCHG9vRo0cUU6facR01/yOlu7fl0npgD1ZxKetDOhETat62COFrkgR8rKQEJo12MffxzTSqkcO8efn072/wgmUO75NGmQsWE7n1J/71bgg1a3qYPrmIgja9TP1I6e7dFsbespP4Ym9Px/GH1AMIcTqSBHxs8rNF/OPf3VlNV3SNTnS5MMvokLxO6oVcf72bFStyeeq6TbQs8n542ranUrDeXB+ef/xhYcCASJZktCGjzon5FqkHEKJ8kgR86MMPQ/nlne1l4+8RuwP3rrRGDXjgtZY4z/MOEyWTQI8hHfnuO3OUkuzfb6F//0j27LHy8NOhsNa/8y1CmJUkAR9JSgrhn/8M40BMK/LPP1HpG9B3pQ4H+UlLOTR/MZ+MWM6+rGjuuy+CQYPCydiZG7BzBQcPWrjxxkh277YycmQhjz1m3HyLEGZjjts8k9Hayv33RxASAjM+sOG8aCkFlSz+MozDgaVrJ4Z1hb/1z2PEiDCWfFtIyPeJxJSk4I6LD5y7a6eT7JUp3Dm6Azt3Wnn00UKeeEIeBRWiMqQnUMUyMizceWcE2dkWpk0r8BYomfSuND6+hPnz85nx0AZUyYm5gh1fa4MjA5xOoq/sScs7ezF3ZxdGDD7C00+7vMV2QogKkyRQhQoK4N57I9izxzsscdNN5t+20GqFa5+IK1ukLpkErn6sI0OHhnPwoDGfuB4PJL2RSvjOVMBbcT3qhs2SAIQ4C5IEqorTyfS7t5C8Lp/+/Yuq17CEw7tIXeaCxeycm0SLNhF89lkoXbtG8dbLLjyr/DdXcOSIhfvvD2fgyx3QlhMrghb7quJaiGpO5gSqgtMJnRKZfETzYHgCoRN+wmIx19DPGZUOaXUCFl2Rx5w5ofxrgoubpnSn3pQUjtRTOH9aQmQ937X7hx9CePTRcDIyrHTpYsE5eQmZ+bIiqBDnQnoCVWD395rYI95x8uYFKUTtCszHQKtKSAjcdVcRP791YvmJOoc093fdzbhxdvburdpxmax9Tmbcs5nBd5aQlWXh2WcL+eqrfJq2jjLlXIsQgUSSwDkqLIQHX7+YZIJvs5LwDieWn0ivrdgR1prp08Po1CmKf/wjnPVJeYSsO7uhIpcLvv/expB73Lgv7sWY/17OZnsnfvzqEMOHuwgJqerWCBGcZDjoHE2ebGe9DuNfd/7Ci3dtCq6hCceJjW6sqhU/2yx89VU+b79tZ/H8QibN70ltUtgTlcDMIctp2y2C9u2LifKUs1+C00nql5pZ69vy2YIYMjMtdGYLCaW9jZauFGpbtuGmk0ENFqL6kU1lOPuNHFatCuHvf4+gWTMPS5bkEhXlg+AqKJA20/B4IHnmBno82bPstS6sYg1dqGHNYWNoZ1oUprAzLIEbm6ziUF40OPNYnNOJVqSQTALX1l1N7wHh3N4vk8seuwLb9tTAqlE4hUB6D86G2eMH87fBiE1lDOsJKKVeBfIAJ9AOeFRrfdCoeCrL6YThw8OxWGD69HxDE0CgsVig9c3xuN+N965B1DyeoSNb0GGri4KkLbT4zXtn37wwhXoZv5FZqwuX199Gq5wTeyuvnbkOT+dOQOQpt9UUQlQNI4eDcrXWowGUUk8Co4DhBsZTKWPGhLF7t5WHHy6kc+cSo8MJPI4/74ncxxFOn5sLwdkC99/ise3w3tl/tPB8cOQSG3Eh7kviy+74Pa1b/elc7g4yBCSELxiWBI4ngFJWvD0CU1i8OIRZs+y0bl1cveoBqtqpPrwdDjIXneLO/i9JQ+74hfAPn84JKKUWAvVPceg5rfX80p+pBXwJDNBaHz3d+dzuYo/NZuxjIUf3OLn7km2syLqQpPUO2rY1NBwhhKiIcucEDJ0YVkrVBN4ERmmtd57p5w2fGHY6KWyXSJMc7V2vfu2SgLljlQkx45m9DWaPH8zfBiMmhg2rE1BK1QVmAE9orXcqpQYYFUtFJX+eSpMcb1FY7BEdsHsDCCFERRlZLLYIaAt8pJRaCgw0MJYzcrthxHvtg7IoTAhRfRk5MXyJUdc+GzNnhrJehzP11l94aWCQFYUJIaotqRiugIwMC5MmhVGzpofHn7fjriuPKwohqgdZO6gCJkywk51t4amnCqlb1zwV1kIIcSaSBM5g/XorH3/srQm4994io8MRQogqJUngNEpK4OmnwwGYNKkQmwyeCSGqGUkCp/Hxx6Fs2hTCgAFF3r2ChRCimpEkUI5je50sGLORepE5PP98odHhCCGET8gAx6k4nUQlJrIoW5NRV4FjCSCPgwohqh/pCZzC/h80jbJKK4MPS2WwEKL6kiRwCmM/byeVwUKIoCDDQX+xZo2VL3+I4WiHlXzxwgaKE6QyWAhRfUkSOInHA+PGhQHwxNhQijtKZbAQonqT4aCTLFwYwpo1Nvr0KZLdwoQQQUGSQCm3GyZMCMNq9TBqlOwWJoQIDpIESs2dG4rWIdxxRxHx8dILEEIEB0kCQF4eTJliJyLCI3sGCyGCiiQB4LXX4MABK4MHu2jYUFYJFUIEj6BPAkePwqRJEBPjYdgw6QUIIYJL0CeBt14uQmWt5p9DjlCzptHRCCGEfwV1EtifmssD717Garry+NzLwOk0OiQhhPCroE4CX47fQQIpAITuSJU1goQQQSdok0BamoVXF7Xj91BZI0gIEbyCdtmIl14KI7sklOWvLaNlxzQy6zWVNYKEEEEnKJNASoqVL76wceGFxVxzUzjU7wIZOUaHJYQQfheUw0FTptjxeCw8/XQh1qD8CwghhJdhPQGl1CNAGyAVuAyYpLVe6evrbtli5dtvQ+nQoZirr5Z9g4UQwc3I++AwYLjWegowExjnj4tOmuRdKvqppwqxWPxxRSGECFwWj8f4ZRKUUk8ATbTWj5zu59zuYo/NFnLW11mxAi67DHr2hJ9+QpKAECJYlPtp59PhIKXUQqD+KQ49p7Wer5RqADwNXAz0P9P5MjPzzimeJ5+MAGyMGJHH4cMnhoJiY6PJMPnEsNnbYPb4wfxtMHv8YP42+Cr+2Njoco/5NAlorXuf4fhB4BGlVC/ge6Czr2L5+ecQli+30auXm65dZS5ACCHAwDmB0iGg43YCLXx2MaeT+aM2EYWTp58u9NllhBDCbIysE2iqlJoKHAbaAf/wyVWcTsKvSGTmXs0LUYrwlksAKQoTQggwMAlorYf74zo2nUz0Xg3AebmaTJ2Mu4NsIC+EEBAExWJu1Qp3XLz3a1kfSAgh/qT6LxvhcJC5cCk2nexNALI+kBBClKn+SQDA4ZAhICGEOIVqPxwkhBCifJIEhBAiiEkSEEKIICZJQAghgpgkASGECGKSBIQQIogFxFLSQgghjCE9ASGECGKSBIQQIohJEhBCiCAmSUAIIYKYJAEhhAhikgSEECKISRIQQoggFhxLSVeAUsoOPA7kAq2BI1rrUcZGdXaUUqOBR7XWdY2OpTKUUq8CeYAT75ajj2qtDxob1Zkppa4C+gOHAI/WeqzBIVWKUqolMB7YADTB+29/nLFRVZ5SKgJYDSzSWo80Op7KUEop4HYgH+gBjNFar/HHtSUJnPAkkKS1XgaglGprcDxnRSnVE4gxOo6zlKu1Hg2glHoSGAX4ZRvSs6WUigTeAi7UWhcqpeYppa7UWi82OrZKqA18orX+GkAp9ZtS6jut9XqD46qs8cBGo4OoLKVUCPAK0E9rXaKUmgW4/XV9SQIn3AHsUUpdAtQBXjc4nkpTStUHbgMmAfcaHE6lHU8Apax4ewSB7lJgt9a6sPT7X4C+gGmSgNZ67V9esuLtEZuGUupuvH/7toDZtg/sBFiA4aU3FUeAd/x18aBKAkqphUD9Uxx6Djgfb1d+Wmn3/lOgp/+iq5gztOHvwEigpl+DqoTTxa+1nl/6M7WAvwED/BnbWaoH5Jz0fXbpa6aklLoRWKi1TjE6lopSSrUGWmmtnzFpD74Z3puJ27XWWUqp2YALmOmPiwdVEtBa9y7vmFIqG+94IsBy4HKlVIjWutgvwVVQeW1QSnUEioAH8A4HRSilngLmaa23+zHE0zrdewCglKoJvAEM0lof9U9U5+QQEH3S9zVKXzMdpVQikAg8anQslXQjUFD67707YFdKPaq1nmZwXBWVDaRorbNKv1+O9wZ0pj8uHlRJ4AwWAy0AjTcz/x5oCeB0tNbrgHUASqnzgfu11pMMDaqSlFJ1gWnAE1rrfUqpAVrreUbHdQYrgWZKqbDSIaHL8CYxU1FK9QUuBx4BGiqlmmmtVxocVoVorScc/1opFQ44TJQAwHvzWeekm85mQKq/Li6riJZSSjUGxgK/A62A6f6ana9KSqkLgAeBh4AXgVe11qYY31VKbcB7Y3K8B5Cjte5nYEgVopS6GrgJyACKTPh0UAcgidKbCCAKmKG1nmlYUGdBKTUAGArY8cY/x+CQKqx0GK4X3n9DTYHhWut8f1xbkoAQQgQxKRYTQoggJklACCGCmCQBIYQIYpIEhBAiiEkSEEKIICZJQAghgpgkASGECGJSMSzEOVBKvQA8XfrfMmA2MPPkKlYhApkUiwlxjpRSk/BWef4baKe1/pfBIQlRYdITEOLcPYd3yYWngD4GxyJEpcicgBDnSGvtAtYAbTDxMtIiOEkSEOIclW5o8g0wHT9uBiJEVZAkIMQ5UEo9AjyPdzeo34E+Sqk5SqkoYyMTomJkYlgIIYKY9ASEECKISRIQQoggJklACCGCmCQBIYQIYpIEhBAiiEkSEEKIICZJQAghgtj/A14fDe5n2+QSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_5\n",
    "# title: Regression using individual functions\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "02481bd5-c737-46bc-9b90-5554fcad8745"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "6bf80137-3a52-483b-a557-b092bbf23b36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.933347799794049e-33"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((f(x) - ry) ** 2) / len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "uuid": "86f9a92c-600d-4515-b34d-20c9f35a86b0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.26243218e-17, 5.00000000e-01, 0.00000000e+00, 1.00000000e+00])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Noisy Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "75d3a6a6-a940-4a49-b35d-29f21880ab95"
   },
   "outputs": [],
   "source": [
    "xn = np.linspace(-2 * np.pi, 2 * np.pi, 50)\n",
    "xn = xn + 0.15 * np.random.standard_normal(len(xn))\n",
    "yn = f(xn) + 0.25 * np.random.standard_normal(len(xn))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "f6f9c05f-1f96-48ee-aaca-f4d80c3d3ac5"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xn, yn, 7)\n",
    "ry = np.polyval(reg, xn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "9a475222-3bfd-4300-951b-94e60792c6da"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'f(x)')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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T80z3DzynVsiQtzZScsFQDumH3UNeXg/gRElAJEslU8TNzTLGTuMGASBIMwOybAFaMhvo\neHk9gBMlAZEstXp1kAnVD1FFEY0EqaKIuntXdZt6GO8bezp3BnMaKO2q47RSL+9UlmgDnWytrKok\nIJKl3l1QyUouoKh1+mcRG3igZSpPX/7fSV8jnTuDtbVCao8dR0tuEKd1yR27jby6U1ky3TyrVwc9\nvR7AibejExFHPztofszjP4rcntTPJ/PB1tdv5h0HSj8+alzs9xx2JANPH89hR4aZ94dT+eK2hz3X\nn55MN8899+R1O+al9QBOlAREslRfF2wl88HW12/mHRPN3P03xnzPwJ3vMeTvm8hpaeZENrCSC7jo\nJ2NoWuGNsYJku3liDbB7aT2AEyUBkSyV7IKtWJL5YEvFTJeOiaY8cgEfLOo8SN08YmTMn/tc5F2G\nz/LGoHGyYy/Zqn/8K0R8yGngteOCLSfJ9F/3daZLrEQzZ/OFnQapcz78IO41chd0r0WU6cHjVIy9\neJmSgEiW6sv0z0T916mY6ZJMomkaHb/VEtrevWsr04PHfR178TqVjRDJYvWTS3o15z/RzmAPPUTM\nD/BLL21k9OiWpO4RL9G09ZP/ZfwN/NPWS7q9r90JnZNEWxdVY2OAsrIBXHZZY1Kx9EV/L5anloCI\nR7k5Z/5Xv+p+rKczXZIZKL2x6kJKKedtjo55ja5dW8l0Ua1fn8MTTyQdZkyhyor2GUtOe0EmM/aS\nDdQSEPEoN/ekXbeOjGzUHm2RTAImUVtZQf7SRQf2NO5SfK2hAWrvXkUVt1PIZjbXFPLMv93A5Ae/\n1emay5blsWULrF3r+PkdV9fCd9TH3hg+mbGXbKCWgIgHZWMNmr5KVIto008ruav2wk4DtJf/ZRq7\n71zV/p6257ZlC71+bk6F7yKhgRkvvZEJSgIiHpSNNWjS7djyX8Y8HuwwgygVz82xr7+5yTFBZTMl\nARGPydYaNOk2qnFzzOPH7d8CpO65Oc1Y6i9jAF0pCYh4TH9fnNRbiRbHOT233Xeu6rS72aAfXx93\nt7O/jL8h5n22fze5gnjZxtX/VcaYI40xvzXGvOxmHCJe0t8XJ/VWosVxTs/NzL2U4JZNBJqbCW7Z\nRP5v7+r0ums567YZSx2TSSnlXPXcRRn5d2aa27ODzgJWAye7HIeIZ8RbnFTDNzMcjXe0bd/oNIPI\n6bklI3/povbrdJyxtAc4CojOmPV2DaDecjUJWGsrjDH/6GYMIl7T3xcn9UW8xXF9eT5+frZutwR6\nJBzOJxjM3OKZgoIhGbtXOih+d/U6/sJC2LCh2+FAYWFGn0nWPX+H55aMTD/bZGQqnqxKAjU18Ze6\np1JBwZCMLJZJF8Xvrljxr1+fw549ASZOjL34qE3o6us6L1ZqVXvVTOoz9Eyy8fk7PbdkZPLZJiPV\nzz9eQvH3dAORDIpX+CxUWdE+YyV/yULqLpvhyr7A2axjQT1an9tTl97fbZB3KVd3en33hN/5+tkG\nIhGnTd/SzxhTDFwMnAvcCSy01jqOvuzatTdjwWbjN6GOFL+7usa/c2eAU04ZRGNjgPnz93cqfNat\nTEErNz/4+8vzP/fcfF59NX4XcjAY4dln65IujJcJaWgJBJzOuT0w/CzwrJsxiGRC15WsU6Y0Eg5H\nzzmVKeg4Y0V6p2u11FhJoWtlU7/JqjEBkWzktJJ1/vx6QLOBMilRCW0/0piASJol2lylL9tEivSV\nkoBImiXaxasv20SK9JW6g0TSLFEXxN5JJVw/NMSVtf8RrZNPIesmXM/kyd+K+3MiqaAkIOKy1auD\n3F07lbuZ2n4s+NcI497w1owV6Z/UHSTiskTdRSLppJaAiMs0Y0XcpJaASIa4uXG8iBO1BEQyxM2N\n40WcqCUgkgF+3DhesoOSgEgGvHZjJa80nkQjQb7509NpWlGR+IdEMkCNUpE0y324goseO1Ag7gvN\nG2DWdGoHodpA4jq1BETSbMBNc2Iez5szN8ORiHSnJCCSZoNr3ot5PLTz3QxHItKdkoCIiI8pCYik\nWctRI2MfHxH7uEgmKQmIpNm+ubfEPj4n9nGRTFISEEmzjnvfas9g8RpNERXJgPrJJfrQF09SS0BE\nxMeUBEREfExJQETEx5IaEzDGDASOAwqAPcBb1traVARgjDkb+A5QDUSstTen4roiIpJY3CRgjAkD\ni4ApQBPwKXAQkG+MeQa4zlq7rbc3N8bkA/8FfMFaW2+MWWWMmWitXdvba4qISPIcu4OMMUOBFcBq\nYIS19lBr7dHW2gIgDPwHsMAYU9iH+48H3rbW1re+/h9gUh+uJ+KKUGUF4eLxDBseJlw8HlaudDsk\nkaTEawkcDVxsrf246wlrbQPwnDHmBeCMPtz/cGBvh9e1rcdiCofzCQYztzNTQcGQjN0rHRR/hqxc\nCTMOVAkNbtkEF1xAQXk5lJa6GFjfZM3zd6D4k+OYBKy1G9v+bowpsta+3vG8MWaKtXYV0W/vvVUN\ndPyXDm09FlNNTeb2Yi0oGMKuXXsTv9GjFH/mhG+5NeYvUtPPbqNmYnY2bLPp+cei+Ltfz0mys4P+\n0xjTfhVjzD8At/cxLoAXgWOMMaHW118GHk/BdUUyJnfb1h4dF/GSZFcMvwEsMcY8SPSD+nvAjr7e\n3FpbZ4y5gmiS2QW8rkFhyTbNY8ZGu4BiHBfxumSTwByi00OfIzpF9FSiM4X6zFr7J+BPqbiWiBvq\nZs5maIcxgfbj185yIRqRnkk2CTwDDAL+DbDAL4AQcGF6whLxjvXrc9izJ8DEic0xz9dPLqEWyF+6\niNxtW6Mtg5/+hPosHQ8Qf0k2CXwCFFtrPwQwxlxJdOqoSL+3bFkeGzfmUFxcR9DhN6ZrgbiCgiGQ\nxQOT4h/JDgxf2ZYAAKy1+4Gr0hOSiHfs3Bng0UeDbNuWS1nZALfDEUm5eIvFzjTGjAew1r7S9by1\n9m/GmBHGmH9JZ4Aibrr//gE0NgYAWLAgRE2NywGJpFi8dQIvGGOWG2MuJjpw+w6wDxgIHAmcBZxO\ntKSESL/T0ADLlx/49l9TE2DBghDz59fHfH+isQMRL0rUHbSP6Fz+fyU6BvAa8CRwE7AL+HqqCsmJ\neM3q1UGqqzv/ipSVDeCNN2L/2ixblsfcuSGamjIRnUhqJEoC+621y4FN1toR1tqQtfZwa+2XgeoO\nNX9E+p177snrdqypKcCcOaFuxzV2INkq0ewgY4yZDhS1dgt1dBHw+/SEJeK+NWuSL1PSdexgxox0\nRSWSWolaAvOBLwEjgQld/oxIb2gi2SHW2MG8ee7FI9ITcVsC1trngeeNMd+x1v6h4zljzHfSGplI\nlog1dnDnnVBamsPo0S0uRSWSnKTWCXRNAE7HRPwo9tgBMccORLwm2RXDIr4Uqqwgf8nC9nIQdTNn\nd1oZDLHHDqKlgD/LVJgivaYkIOIgVFnRqTBccMsmhs6YTi10SwQi2SrZshEivpO/ZGHs40sXZTgS\nkfRREhBxoM1ixA+UBEQcOG0Ko81ipD9REhBxUDdzduzj2ixG+hElAREH9ZNLqL3rXpoKxxEJBmkq\nHEftXfdqUFj6Fc0OEomj62YxIv2NWgIetH59DmvX5vb4nIhIT6kl4EHxtjNMZqtDEZFkqSXgMfFK\nEqtcsYikmmtJwBiTY4yZYYypNsaMcysOr4m3naG2OkyPUGUF4eLxDBseJlw8nlBlhdshiWSMmy2B\nk4B1QPJF2/s5p+0ME52T3msrDRHcsolAc3N7aQglAvGLQCQScTUAY8zfiW5TuTHRe5uamiPBYP8d\nFF2xAqZN63wsGIQNG+CVV5zPjU3x2qV162D3bjjvvNRe15OOPhrefbf78aIiqKrKfDwi6RFwOpHW\noUVjzJPAETFOzbHWPtLT69XUZK7REK0CuTdj9wNYvDgf6Jzkmprg6qubqKkJOJ4rL+9erbIv8f/i\nFwPZuDGHk092b/A5E88/VFnB0FgJAIhs3sxHfbi/G/9/UknxuyvV8RcUDHE8l9ZfcWvtOem8fn+T\naDvDUGUFg26ZQ8777wHQctRI9p1/C/Wkbh572+BzY2OAsrIBXHZZY8qu7TVOBeJApSHEPzQ7yGOc\nBinb+q5z33+PANG2Xe6O91Lef+2nwed4heBUGkL8ws3ZQWFjzE3AwcDlxpgvuRWLV8QbpIz3rbVr\naeNQZQUUFfV4tovfBp8dC8SNGKlVwuIbri03stbWALe2/hHi16+P962147mOG6EE6NlGKLH2yi0r\nG8Cllzb2i71y16/PYc+eABMnNgPRAnEdN41ps2/OLZkOTcQ16g7ykHj16+P1UXc855RIBl19BYcd\nGb9lEHuv3EC/2St32bI85s4N0dQUfV0/uYQVX19OFUU0EmRjbhEfLFKBOPEXFR7wkOYxYwlu2RTz\neN21s2J+a4XO/deOiaSxHoCcOC2DRAPT2SzWgHdDA8x+6UKqaZ172wyXbW5gPvXuBiuSQWoJeEi8\n+vVtZY2bR44kAkSI9l13LW2c7KwWv22R+NqNlbzSeBKNBPnmT0+naUWFY/fXG2/o10L8Qy0BD6mf\nXEItB8YA2loAbR/yyZQ1durn7spPWyTmPlzBRY8deCZfaN4As6bz7udDwNRO723r/oq19kKkP1IS\n8Ji+1q/fO6mE64eGuLL2PyhkM00EOYj93d7np3nwkdtit3puCv6cWdXfyHA0It6idm8/s3p1kLtr\np3IyVeTRyKXcF/N9278bu+upTbbsW5BMnAfv2BLzeGj7gdZQtvx7RVJNSSADMlmlsusMnwcppZTy\n9hkwVRRRSjlXPXdR3Ot0nUnjVUnFeYJDq6fD8Wz594qkmrqD0qzjvH3o2bz93mib4dO59sgkYBJ7\ngKOAXwHg3OedLaUjko3TaZykbVZVtvx7RdJBLYE0i7cAzItClRUcNmE8dY0DqKKI7bdVerZ0RLwS\nFx1bX/lLFlJ32QzHDeP9VCpDpCslgTSLtwDMa9paLcM/2kiQZorYwG/3TeXdyT9yO7Ru4pW4iFV+\nI/+3d1F37Sw+2rGbmmdeaE8AfiuVIdKVkkCaOdan8eDsHKdWy8TNv2H3nasyHE188eb496T1pbUC\n4nf6n55m8RaAeU281klwgbe6r+KVuOhJ66u/l8oQSUQDw2nWdd7+ZgpZN+F6Jk/+ltuhdeNUtgLg\nuP1b+CjD8cQTr8RFc7Fz+Y2eXEfED9QSSLOu8/ZPpoqr/nqhJ7sbnFot4M3uKyfZ1PoScZv3Pomy\nWKwFR+nobkjXwqb6ySXUXTYj5rm2D9BMrnlIxCkWVQcVSZ66g1Jo2bI8Nm7Mobj4wN686ehuiHWf\nVNk3fwFN/3BGzPpFmV7zEE+8WPZOKlF1UJEkqSWQIm0LjrZty6WsbEDiH/Dwfeonl1DzzAvdplN6\nac1DvFg040ckefqtSJFYpYrTwc2FTYlm3WSyqyheLJrxI5I8JYEUiJYqvpgiNhCkmS80b2D4rNRu\nAA/uL2yKt+Yh3v7IfeGUWOLFsmZNHdXVe7v9UXloke6UBFLAqVRxborn1rvdzVF7tfOsG6fumSE/\nuKLXLYN4iUUzgERSQ0kgBZIpVZwKbndzrIxRkfTCnN+zcdz5jt0zgfr6HrcMQpUVUFTEEIfNcfKX\nLmrfac2pHpCIJMe12UHGmMVAHfApcBIw01r7oVvx9FaosoLcUBDqm7ufdCph3EtuL2y65548XqWU\nByk9cLAFds5pYk2chWYdtX2AO+k46yfg8J62hNPXDXhExN0povustTcBGGP+HfgJcI2L8fRY12mK\nXfW3rol4Saj24dkcelXft7V06lbqKJsWrol4nWvdQW0JoEMcn7oVS285fWBFQgN91zXRtavoMwbG\nfF+iD/Bkqqv2t+Qq4qZAJBJJ28WNMU8CR8Q4Ncda+0jrew4BKoEp1trd8a7X1NQcCQY9tAVgMAjN\nMbqBgkFo9NfGJGecAS+9dOD1d1nJSi7o/sbycigt7X68TVERbNjQ7XAE4MQiAj++Mf7Pi0gsTr2r\n6U0CiRhjDgbuBH5irX0r0ft37dqbsWA778wVW7h4fMx+8KbCcdQ880K6QktKMvGnW6iygt03LGbE\nJ1ugcCyfta48TvQzsbrYSinnpPnfzppdv7zw/PtC8bsr1fEXFAxxTAKudQcZY4YBvwaut9a+ZYyZ\n4lYsvaVpivG9c+a/MKYuWjjvlxe9nFT3WNusH4qKiASD7Cg4kVLKeZBS7folkgZuThF9CigCHjDG\nPAN8z8VYekXTFOPr7erm+slN/qhaAAAH1UlEQVQlrLu7igfu+4QvBl5rn42kXb9EUs/V7qCecqs7\naP36HPbsCTBxYoz+f49yuznc0ACnnDKo0+K2yy5rYP785Iq4zZw5hKefbuHDDzt/TwkGIzz7bB2j\nR7ekNN5Uc/v595Xid5cvuoOyybJlecydG6Kpye1IskdfVjfv3Bng4YfplgBANYBEUk1JIIFMVQft\nb/qyujnajRT9ezgcwVrVABJJF+0nkEDXfu0pUxoJhzu/Jxu7i9Ktt6ubnYrkJduNJCI9o5ZAHMlW\n7VR3Ueq4XSRPxG/0mxVHMh9I6i5KLbeL5In4jZJAHMl8ILm5yUt/1LYXQCSCxgFEMkBjAnEk6tdW\n/7WIZDu1BPpA/dciku30aZVAvH1z1X8tItlO3UFxdC1m1rY7Vi3R0gZub/IiItJXagnE4bRfQP7S\n1O4dLCLiFiWBOJw2OElm4xMRkWygJBCH0y5Y2t5QRPoLJYE4tF+AiPR3GhiOIVRZAXcsZsjmzTSP\nGAlAzs4PaR4zlrokdscSEckWSgJddJwRFABy338PQJvFiEi/pO6gLjQjSET8REmgC80IEhE/URLo\nQjOCRMRPlAS60IwgEfETJYEu9k4qYcbQB6iiiEaCVFHE3RN+p0FhEemXNDuoi9Wrg9xdO5W7mdp+\nLPjXCOPeqGP06BYXIxMRST3XkoAx5lrgRGAb8GXgdmvti27F0yZeZVBtbCIi/Y2bLYEQcI219jNj\nzGTgFuBrLsYDHNhIpqBgCLt27XU5GhGR9HItCVhrf9Hh5Shgs1uxiIj4VSASiaTt4saYJ4EjYpya\nY619xBhzJHAj8EXgO9baj+Jdr6mpORIM5qYhUhGRfi3geCKdSSBZxpivEh0TOD3e+3bt2puxYLO9\nO0jxu0vxu0vxd7ueYxJwbYqoMeb6Di/fAo5zKxYREb9yc2D4aGPMQuAj4CTgMhdjERHxJTcHhq9x\n694iIhKlFcMiIj6mJCAi4mNKAiIiPqYkICLiY0oCIiI+piQgIuJjvkgCocoKBp4+nsOODBMuHk+o\nssLtkEREPKHf7ycQqqxg6Izp7a9ztmxi6Izp1II2ihER3+v3LYH8JQtjH1+6KMORiIh4T79PArnb\ntvbouIiIn/T7JNA0emzM481jYh8XEfGTfp8E/jL+hpjHt393doYjERHxnn6fBG6supBSyqmiiEaC\nVFFEKeVc9dxFbocmIuK6fj87KLpn8CRgEnuAo4BfAaBN40VE+n1LQEREnCkJiIj4mJKAiIiPKQmI\niPiYkoCIiI8FIpGI2zGIiIhL1BIQEfExJQERER9TEhAR8TElARERH1MSEBHxMSUBEREfUxIQEfGx\nfl9FtC+MMXnAbGAfUAh8bK39ibtR9Zwx5iZgprV2mNux9IQxZjFQB3wKnET03/Chu1HFZ4w5G/gO\nUA1ErLU3uxxSjxhjjgduBV4FRhL9P3+Lu1H1jDHmIGAd8JS19odux9NTxhgDXEC01HExMM9a+1K6\n7qckEN+/A89aa58DMMYUuRxPjxlj/hEIux1HL+2z1t4EYIz5d+AnwDXuhuTMGJMP/BfwBWttvTFm\nlTFmorV2rdux9cChwEpr7WoAY8xmY8zj1tr1LsfVE7cC/+d2EL1hjMkFFgHfsNa2GGOWA03pvKeS\nQHxTgXeMMacAh9G2FUGWMMYcAZQCtwOXuBxOj7UlgFY5RFsEXjYeeNtaW9/6+n+IbmaRNUnAWvty\nl0M5RFvCWcEYM43ocy8CBrscTm/8AxAArmn9UvExsCydN/R9EjDGPAkcEePUHODzRJv0S1qb+Q8B\n/5i56BJLEP+3gB8CB2c0qB6IF7+19pHW9xwC/BMwJZOx9cLhwN4Or2tbj2UlY8xk4Elr7Va3Y0mG\nMaYQOMFa++NsbLW3Oobol4kLrLWfGGNWAA1AWbpu6PskYK09x+mcMaaWaN8iwPPAV4wxudba5owE\nlwSn+I0xpwGNwAyi3UEHGWN+BKyy1r6RwRDjivf8AYwxBwO/AaZba3dnJqpeqwaGdHg9tPVY1jHG\nTAAmADPdjqUHJgP7W/+fnwXkGWNmWmuXuBxXT9QCW621n7S+fp7oF8+ydN3Q90kggbXAcYAlmqG3\neykBxGOtfQV4BcAY83ng+9ba210NqoeMMcOAJcD11tr3jTFTrLWr3I4rjheBY4wxodYuoS8TTWBZ\nxRgzCfgKcC0w3BhzjLX2RZfDSshae1vb340xA4HBWZYAIPql87AOXzaPAbal84aqIhqHMWYEcDOw\nHTgBuCOdo/TpYIwZBfwbcAXwc2CxtTYr+niNMa8S/aLS1gLYa639hoshJWSM+RpQAuwCGrNwdtCp\nwLO0foEABgG/ttaWuRZUDxljpgBXAXlEYy93OaQeae2G+yrR/0NHA9dYa9O2KbqSgIiIj2mxmIiI\njykJiIj4mJKAiIiPKQmIiPiYkoCIiI8pCYiI+JiSgIiIj2nFsEgfGGN+BtzY+uc5YAVQ1nH1qoiX\nabGYSB8ZY24nurLzbuAka+1Sl0MSSZpaAiJ9N4domYUfAee5HItIj2hMQKSPrLUNwEvAiWRx6Wjx\nJyUBkT5q3cjkUeAO0rwBiEiqKQmI9IEx5lpgLtEdoLYD5xljyo0xg9yNTCQ5GhgWEfExtQRERHxM\nSUBExMeUBEREfExJQETEx5QERER8TElARMTHlARERHzs/wGuo9qOj4ok6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116b43c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xn, yn, 'b^', label='f(x)')\n",
    "plt.plot(xn, ry, 'ro', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_6\n",
    "# title: Regression with noisy data\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unsorted Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "uuid": "8ea85cdb-47f2-4967-b684-7894d9964e76"
   },
   "outputs": [],
   "source": [
    "xu = np.random.rand(50) * 4 * np.pi - 2 * np.pi\n",
    "yu = f(xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "uuid": "0034edf5-1cef-4eea-be44-c69103fe6eb2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.33  2.34  3.39  1.35  0.36 -5.68 -2.29 -3.37 -4.55  5.31]\n",
      "[-1.64  1.89  1.45  1.65  0.54 -2.27 -1.9  -1.46 -1.29  1.83]\n"
     ]
    }
   ],
   "source": [
    "print(xu[:10].round(2))\n",
    "print(yu[:10].round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "uuid": "d7f5f003-1cb8-4432-a8d6-cb4bef1a101a"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xu, yu, 5)\n",
    "ry = np.polyval(reg, xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "uuid": "40177962-0363-479c-bdbd-451a4c043060"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'f(x)')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EGgxG+Otf92XMzJR1k4rY9cZbbdoLOpuw7qSGtzo9X6DeoVung656Ld1wQwia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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116c2f400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xu, yu, 'b^', label='f(x)')\n",
    "plt.plot(xu, ry, 'ro', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_7\n",
    "# title: Regression with unsorted data\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiple Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "uuid": "82b95a7b-9e3e-4dc8-b313-1af775b06b8b"
   },
   "outputs": [],
   "source": [
    "def fm(p):\n",
    "    x, y = p\n",
    "    return np.sin(x) + 0.25 * x + np.sqrt(y) + 0.05 * y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "b03b67ac-f7df-41d1-9dab-1e074e8738fa"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 10, 20)\n",
    "y = np.linspace(0, 10, 20)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "  # generates 2-d grids out of the 1-d arrays\n",
    "Z = fm((X, Y))\n",
    "x = X.flatten()\n",
    "y = Y.flatten()\n",
    "  # yields 1-d arrays from the 2-d grids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "52a91ef7-33c4-4de1-b69b-ea4d740aa252"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x116ef55f8>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nLp7ZR3Axvpmdf9u7kLlcy9/tVNF+4xvfwgsvPMe5c4/w6quvcPr0mR1nZQOo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116cec630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib as mpl\n",
    "\n",
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=mpl.cm.coolwarm,\n",
    "        linewidth=0.5, antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: sin_plot_3d_1\n",
    "# title: Function with two parameters\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "uuid": "5918f2cf-3ead-4b80-980e-4a375ee159db"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((len(x), 6 + 1))\n",
    "matrix[:, 6] = np.sqrt(y)\n",
    "matrix[:, 5] = np.sin(x)\n",
    "matrix[:, 4] = y ** 2\n",
    "matrix[:, 3] = x ** 2\n",
    "matrix[:, 2] = y\n",
    "matrix[:, 1] = x\n",
    "matrix[:, 0] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "uuid": "48ce242e-3411-41bf-b6c1-c8e228f3e494"
   },
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'statsmodels'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-1-085740203b77>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mstatsmodels\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapi\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0msm\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'statsmodels'"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "b9eb74bd-9280-4d8b-ae7d-8853911389cb"
   },
   "outputs": [],
   "source": [
    "model = sm.OLS(fm((x, y)), matrix).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "uuid": "cc9c9f77-9051-4d82-bb7b-c646216d542f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "uuid": "b68898de-9001-4a15-a5ee-7ee50c5592ea"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6.38378239e-16,   2.50000000e-01,   5.55111512e-17,\n",
       "        -2.60208521e-16,   5.00000000e-02,   1.00000000e+00,\n",
       "         1.00000000e+00])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = model.params\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "uuid": "1f5d1574-8238-45e4-987d-bdb7cc6b5e03"
   },
   "outputs": [],
   "source": [
    "def reg_func(a, p):\n",
    "    x, y = p\n",
    "    f6 = a[6] * np.sqrt(y)\n",
    "    f5 = a[5] * np.sin(x)\n",
    "    f4 = a[4] * y ** 2\n",
    "    f3 = a[3] * x ** 2\n",
    "    f2 = a[2] * y\n",
    "    f1 = a[1] * x\n",
    "    f0 = a[0] * 1\n",
    "    return (f6 + f5 + f4 + f3 +\n",
    "            f2 + f1 + f0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "fd9f8eed-1b10-4ec8-8a15-bedae7f53a18"
   },
   "outputs": [],
   "source": [
    "RZ = reg_func(a, (X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "096451ce-173a-43b5-b81f-9dac26df2702"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1c1b66ea90>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Dkz464rvXB9f4VaD4+rIEP1U7Tnc0yh98Ns773nCCc93VJX73KuNGzeoGjzwz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HktqhpA14vExsYR55gtLSlFotHmT77FYhaPUpsIq0qIbMYkmRyiv6+n7ilZQ8OjKHL9+Vv7xB8l\nFiuAGKe3u2decYwnnJkUpusJVvRNLyjLF4oMj0zg9UZR1ak1eJQ40Uj14jNdNzg9GEdSg4iizJqV\nja0v4PcT8NtClCyYxEdTZLMZLtxQm3d6sxw7m6a7wuAnGokwkSuQzKZZ2VN9A/nr3x3gj15zIZGQ\nD02bv3hsIWaKuCiWhLsk4lBZ3GYYBvl8YXJOO5OvUTsvHg4HyxXqU1XqmuOnuMZy2m54fD7ck/Yy\nw4nweOl0ncsVKBb1yesKDV/3qX0j7DpUYEXfatLpOLmUjijMkaMUTLp6wk2v3zTNyR7Z2ou1BEFE\nkSMMDo7T0xOp+Xvj8Tiy1NxpUBQVQGFwMEYgIBONzt4AZLIp/L7mC7tMU6O3ZyqMr2kag8MxFCWM\nzzddcC0zy/oqYfFiUef0cAKPJ0wg1INhaHQGnakPEEWRfMGgp3c1R88miPhNejqdG+c5k5FYhs45\n2vG8Xg+mqXDw5Bhb1s7+HR88PkzEZ3H1RT2oqkIwGMA0jbJQNiviYAtxpYiXXt8ej0oqZcfNpyrU\nZxa32Rtte21TFeql6vRiUWt6fW4hmvO0x0l7cXBFm+ZEWxRFAgHvpKvZ9Nx1o61kE6kC3/rPw/R0\nXUFsfBhL9yEIc7+5B6NW2Se7GdLpGF5vY3lfVQ0xPp4lFCosOK/bMDSyWQvZgXA1gKIEKBQsTp8Z\noqc7gsdjPxamaaIVDbxzTM6q+x5yFo/ag67bYi3LIbze2cJsWRZ93dYsN698ociZ4RR+f5RQaOpk\nKhgTBByybM3lC4RC9mMfiUQwTZMDx8fYuCqI6sBUtkoMwyJTkIh45n5sRVGko7OX/SfG2LzSjzJ5\n/6Km89iOg3zi1m3TTrt23lnG41EJBv1YljVNxOst2pqJqiqEQgGy2TyGYRf0zVehPldxmx1O9xKJ\nBDEMc5qIN1JU5oq2sxjLKN3gijaNV497PPYgklyuWMXoob4pX/ZaLP73/92N17eOifEE4qzpylPI\nngKRcH99i56DXD6Np8nBFLLsJZs1yBfG6J6ngn1waAxVcaatqUSpSG5iQsdiiL7eHiYSMQI+J8Li\nKXr6Ojh9dgRR9OPxVL+mKk9Mm82t6wYnzsYJBDoIz3BDy+cm2LjauWKxWDI3bRSmKNrTwwYncmAk\nWbfCmfGeAMfOJujsXDgd093VzcmxFF1BjWjIy//bdZhXXNlHT3T6JrOUdwZbxCVJKgtlIODDsuzo\nhn3i1eedfjcTn8+L1+uZtAm2I2D1VKhXFrdlMjkAZFlGVWW8XpVwOIBpWuWceLGoYyzgaVlvv3ir\nZiOcT1hu9fjyot4XhSgKk28mFqlUtmpRSSObgYeePs3guIpH8iJWOV0DCIJOV0/zomSaBqZhIdUx\nxan6miQsw8/ZwUH6+/pm5ZpjE7EF27uawbZ2jXD61AgmBoaWIBgM1p1vL2GaBqZZZGg0i6rOH4Ww\nzCwb1k/9PmLxNKmsOEuswY429HU65y0+OBKju3PujZI9G9zHwIkYK7tkQsHmetUT6TzhcO3Pu3Ao\nRKZY5NThIYaGx/jT1y1cfGYYRjn3DPYGxG7lkvH5vNOE1Bbx2SIpCBAMBhBFkUQiOW/hV70V6rpu\nW6pms7YXuyRJZec2u9hNqBDx2RXq7dIvfj7hhsfPQ5zqxS6drvP5IoWCs4MtzoxleODhk3jlixEW\n+NWEOyXkubxJ6ySdnmg4LD4ngoAiRxkcHKWvr2Ny5jRoWpFCXkSSWntisEwTTbNQ5DD5LOQyGQwz\nhyiZeDwqoWAYWZktmIV8jmwuS7Go2W8Alow/YNHV1bfwPSvC4qZpceJMDH+gC38VS08nw+L5QoHA\nAikJgM7OTtKaztDJGJtWhyfzvvUzGjfo7KjvbUNRFHbuPc57X3tBzS1hlZimOS3vXCrwlGW7H9tu\noTLQNK2cEw+Fgui6TiKRqvt+9VaoG4ZBLmfMsF+1ndv8fi+iOGW/Wixqbni8BSynx3PZiHaziKKA\n32/v8uc7XTeKbph8/Sf7UIT1Cwq26isQDDYfFs9mk3jmae9qBlUNMzKaJhK2DVGGR2KoSutbkdLZ\nCRR5SsQEQUKW7EpmrQDj+QKGGUcQSsWCEqLgmTylexHwIouAkKOzyul1JqWweDKdYyyuT8tbzySf\nnWDjGufC4uPx3Lxe9JXIsky0o5ejg0n6ItR96j52JkFnR/1zsg8cPsa2dT62rHHOU71Q0Mqb5lLx\nmKLIhEL26dowTEzTRFHkptu46q1Qt+1Xp3L2U/arCuFwAEEQ6OgIl0V8oeI7Owrghsfnwz1pL0NK\nL7i5Xjz2wILGTtfzXbeSnzx6jMGxAD5l/lOTIGp0dTfvemaHFKWW5soU2Uc6rROLncLjaX7NC6Fp\neeS5KuwrsK1R56+qtiyTjk5fTfPDLTPL+nWdnDwbQ1EjhILV72+aOn0OjtwcGp2o22gGIBIOk8gX\nSOXmb82qJJsr4vXXL7qZbI7DR4/wudsvr/t7a6VUPCbLEiCQSKTKQu73+5BlafIkbofTdb01Feql\na84U8Zn2q319XaTT2WkV6oZhVIi4NutQ0IrX6dNPP8mjjz5CR0cHgiBw++3vdfwei8UyOmi7ol2i\nFD6v/OULgkAgUDpd5xqqYp3rujMZOBnnP58YIei5eKGrEekqnQptCoUcuVyWYr5onygEgYDfRzga\nnTeXm8k4HBavgmEYxMdAVgfp7OpDaOHgkVwuiyo3ZvZSierN4/MtXGhlWRbRsMaJsynC4YU3JZY+\n4UjPOEChWMTnb9xMx+OxW7MOnxpjcw0n4NNjBbo767/fk7ue463Xryfgc26zMhNBEAiFAggCxOPJ\nsnjaJ2w772yH02V8Pg+y7HybWWVefD4P9ZKIV6tQ9/nsCnXTNMlkcjz88MNs3LiJ/v41jgp3Pp/n\nnnv+hu9+9wFUVeVTn/oYO3Y8xVVXzT2QqN2ppzjxXMcV7UmmitHsF5eq2i/wQkErTxlq8MrTrjuT\nbF7n6z/dj0/ZCFQXNNMysYQkyQmF2GjSdvlCQaAkzOrkH0gVIRWPYQkFFFUgEAoQDIbLhWGZbHxR\nBBsgNjqOKAQwNYXR4SG6enqQmhj8UY10ehxVdqBCWsjX7N+u6zFMIUo4vPBEtXwuzoZVzj3mo7EM\nPd3NhdlFUSQS7eXAiVE2z2NBenIwWbXQbT5OnD5Lp1/jhRfVH1KvFUkSCYeDFItaubp7LkrinJv8\nklKbmddrt5mZplWuTneizaxahbrP55127ZkV6lCqUJfQtCK/+c3D3HPP3yKKIpdddjnbt1/ODTf8\nPqFQc5vTvXv30N+/ojxH4NJLt/PEE4+dw6K9fI7ay0a0axvPab/Q7OIRgXQ61/QObqH7fveXB8lk\nu/HI1UO26eQo+Wyeju5+dMMW6YXPqyKC5UMvQKJgEB8bRRCLqF4RfyC0KL/5idgIgjUVLhasAGMj\nMSKdQbxe54ZZaHoBSXDASMSyiHSoC4bFDUMnNjHGls0rZ/Vkz4VpGPR0OJeKGB6LNy3YlXR19nBs\nMMHKTpGAf3pxY76gIan1n7CLmsYzz+3j0390actSMKXwciaTK4eea2XK3nT+NrNSOL3Z9wFBEAgG\nAyiKTDKZnuwVh+oV6gaCIPGJT3way7IYGhrl2Wd3sWfPs2zYsJEXvKB+C9hKJiZi+P1Tr5lAIMjB\ngwNNXXMpcQvRlimKIhEIeCkUNDKZZk7XU8zXTvbUvhF+93yWoLplzs9n0+OkYmlMTaJzdbipYSAC\nMpgy6USCTMIiEM7Q0dW89Wk1ioUcxZw8q3xGxEsyVqAYyBOOOGQsks04EhaXPVn8/vmrxVOpJKlU\nkXVrwzUJNoCpjxMKOPOzFjUdj8d5p7NoJMJ4Jkc6l6Gva2pDdWI4R08Dk+N27dnPjS9aQXek/rnu\nteD3+/B4FBKJ9IJ90bUwX5tZqQB1oTazagiCUO7nTiSSkymz+irUV69ew+rVa3jd6/6g6Z8VoKOj\nk2xpqgqQyaTp6Fic6FsrcE/aywxBEBBFEUkSHTldV1Kt1cx2PTtEQLmQmZWhuWycVCyOUZABCX+H\nhOKAKOlGZtKsRSCbhGz6FF29nXh9zo5wNE2T2Fi8qjGMgEQhYzFeHKSrZ0VT90qnY44INkJh3rC4\naZqMjo4gECQSsV3HaqGQT7C+QW/xuRgeT9LrQCHiXPi8PgxD5ejpcTaujnBmJE33HFalCzEyFqOQ\nHeeGq5wvPivlrwHi8VTLTlhzt5kpyLI8Z5tZtWlhkiQRDgcoFIrlvu65mK9CvRU/4rZtlzE0NEix\nWERVVZ57bjc33/wW52+0SFiuI9rywd5JezBNi3xea0FBw2xXNMuyuO/f92Maq6b1WhfySZLjE+h5\nidKvRpQh6MCJ1LIMLBOEyrWYPsaHMsjeOD19/Q2bkMxkIjYyr5ObjYCp+RkZPEt3Tw9iA3luTS/M\nmnbWGBbhiFz1588XcsTGUyhyGFEssGZ1bREK0zToCjfuPz+T0ViSngaqxetBkiRCkV72HRvG7wvg\nq3Ptpmnyu527ufONFyA12As+39psAdTIZqvnr1tBNY9yRZEJBv2T4z71aXnxUvg+nc5WcUycH/t5\nI9bUxVAvXq+Xj37043zpS39HNNrBpk0XnLP5bHAL0ZYFgmBbHMqyRDqdR1VlR8xXZlIKhVXy8K4z\nHDgOfrVr8msMJkbPUkgBTBeOcK9/wb7tWtD09JwTwkBEz3s4e2KYUIeHSLQ5UcjnMhiFOoaOWAFG\nR2JEOoJ1n/gdC4urWQKBucPi4+Oj6JqKIgexLIv+FZ6aNzdGcRwlFGY0liaX1ygULTTDAiR7Vras\nIooS+XwKRTbp7fITCc4dTtZ0A0lSF83OMpWVyOQNFKWIz1u7ic+e/Ye49qIo61c4EP2owONRCQR8\nDQug08ysABcEoTy7u9RmBlAoFGtu+5x+fbArV1rXo3311ddw9dXXtOTai4170j4PqXy9yLKduy4W\ndZLJzOTnW9OzPHNoyFAsyw/+6wQ+1W7v0opZYsMjmMXZvwpvWMCjNm9+ops5ROY/kQqopCcsMslT\ndPf3oKr15yLted+pBe81ExEvqYki6XSSzq7emkTRsWpx5g6LG4bG8PD45Ona/lggmCMSXjicn0im\niMWSrOjvYTShAB6QwOODubYzwaAdPk9kYGgsjWnkCQUk+rtDyLJ986HROL09ravCrmQsliQc7kIQ\nRMbiOXxqiu7OhUU4nkgyPHiKO25srkhqJoGAD1VVSCRSbXuiqhxyEgoF0HXIZvPIsjR5OJBrbjOb\nEuzWtUeeb7R7Tnvr1q2bgL8CdgGrgfGBgYG7GrnWshHtEn6/B1mWyWTy0/JQlkXD1o7zM1WIZpgm\n3/jZPmTWISCTTo2SHsthmbN/DaIIoQ4nwuImpqEjUlv42TJ8jJ5JEIimiXbUlzuNjQ3XEBavhoil\n+RkbiuENCIQj1e+taXlnqsWxCEeVaZsE0zSJxcbRNWmas1otYfHYRILxWA5VCRGJBJAbCPn7fEEg\niAmcGtHJ5eIIVoE1q1pXNFiJYZjkClLZgtXj8aGbKifOxFi3qnpu3rIsHt+xmztu3kYo4HWs9zkc\nDmBZVkvz104hiiLhcABdN8r2qZqmLdhmNjY2TjKZore31xXsBmnXzVwFncD/HRgY+BnA1q1b923d\nuvXnAwMDO+u90LIRbVEUCIf96PrU6Xo6rZmkU/k+8x//7wSnhjx4pCDjw6copu2c1VyEeucfGFIr\nmpGqEhafD4lM3KKQP0PfilU1fUcum8LUmq8UFlApZGA4M0ikMzxna1g+l3WkMG9mWHw8NkYxD7Ic\noLIwfKGw+OhYjHhCw6OG8agqlpUgHFrYs3whJEnG7+8gmUpx/EyOkN+gv7e1VrAnz8ZmDTkRRQmf\nv5vDJ8bYsDqKNEc/9/5Dx7hkrY+L1kXLed7pIzZnu3zNhyxLhEJBCoXCvAVc7YIsy4TD9vjPUgX6\nTKq1me3cuYMvfOHzKIrK9u0vYPv2K7jiiqtYvXrNYv4I5zTtvqEbGBh4esaHRGAuIVqQZSPapmmR\nzearVnnav/TWhMdFUeTo2SQ//e+zqNYGRgdPYWrVH3pJxRHzE9MqIlqNCqmAnvdw5uQp+letQJKq\nrzSDsCsAACAASURBVNc0DRITWUSca+8R8ZOKFUnJSbq6e8oucKn0+LQTcONMhcUnYuPk8haK7Eee\n48esFhYfGh4nlTbwqCE8qp0SsCyN3h7nWmcm4uOEQ3bERTMsBo6MsW5VGG8deeZaicVTBIPVozvh\ncDcnzibp7ZIJ+qd+1+lMlqPHjnLX7S+Y5rk9u/e5tjnZXq+K3+8jlcqiaUufv16IqfVm6vI5L7WZ\n/d7vvZSf/vSlnDp1imeffZbdu3fxb//2E77+9f8Pea4npMssTL3tT9pltm7dejPwy4GBgQONfP+y\nekZomlG12MypKWBzXVfTDf7u+89i5LqJxSbmDIdX4o8qOLGB0PVcA6fsGRg+Bk8N090frWqIEhur\npVq8EUTQ/YwNTeDxC/j8gQW9xWvBsiwiHQrJZIJsVkeRgyhVfiVzhcWHR2KkUiaqGsAzQztVTwFF\ncaYIq1gs4PdVDj8RCAS6GBwtIjDOegcHjximSSoLwcD8YdlgMEw8VSCdSdLfY6/tdzv38LYbNsyy\nKp3Z+yxJ4oIGJiUv7ng81bQr2WIQCPhQFKXh9ZbC4YIgsHbtBtau3cAb3nCz4+s83zHb/KRdYuvW\nrdcD1wMfbPQay0q056N1g+Yt/uXhI8RHPWjJ2ipBvd7mT5KWZTh28hUsD+ODaYId+VnV5dlMAlNz\nou1qnvujks+YpOJDiJKE6vHg94UQpfpzxqZpYFpJEgnPvGINk2Hx/qmwuK7rnDg5iixHUNXZv0fT\nbKyvuRqpVHrO2dWKogKdDByZoLdHpSPc/Ebm1NnYvNPJKlFVD5alcPTUOJaRZUXU4qqtC9c/GIaJ\nYRTLtsDTDUx8iKI9ISuXK7RkA+0kU/3iU4Yp9eLmr53DbP+cNlu3bn0t8FLgTmDF1q1b1w0MDDxR\n73Vc0Z6kVaJ9fDDFTx4+gZaqrajLEwRRrG9k4lzoRgbB0dOvRHrCpFg4S0/fSsAWwGQ872hYvBq6\nlkQwg1gmFDQopNNYQhFRMlFUFZ8/iCxPPW6maVAs5tGKOXRdxzQsLENElEW6+7sRa3CXCwRzRCJ2\nWHw8FiceN1CUuav5LcukI+p17DmUSMbnFOxp6wtESaUNxsZH2bi2a85cc233yhAI1GcAIwgiihpm\nx45dfPb27Q3dt2RgYpomqqqQy+UxDHucps/nacqFrJWU/M4XMkypjoVllepZXMF2AqdHJTvN1q1b\nrwR+COwAHgECwD8Armg3SivC44Zp8vWf7CUfC4NV28V9IWdOrZYltCBDL1DMqpw9dYr+VSsZHx1u\nPvxeA4aRB3PmxkBAsDxYOhR1KGZzWCQQRAPLtIep2G+IMqWnuYBFpNNTk2CLYpHVq3owTYMTJ0cQ\nxTCKUn0zJYppAgFnKrxN06y5N18UJXy+bo6dyhANmXR31RelMU2LiZRBKFi/sc7+gT28+WVr6Qg1\nvsn0ej34/d5p+eCZLmR2xbXtQlZpYFKtPqWVTPmdZ+se02tjYVml/mtXsJ2i3U/ak1XijY/lq8AV\n7TLOn7R/9dRpDh0xMIu1/a4EEVRP86Fxwyy09PRr6T5OHD6GqgZQWjdx0b6XZaJphZp6vwVUMKsn\nILwhA4+nht+FZdHbp5DJ5BgZzaMu0CtvWgVW9DpnVRqbiBEJ1xdm93oDZAsGJ06Ps2517d97ejBG\nKFi/LerwyCCdviwvvWxT3d9bws5fS1XzwfO7kAUQRXFSwOe3EnUKn8+L1+shmUw3dK/p4fA2j/+f\nYxhLsIFbKpaVaM93mna6enw4luVf/us4erL2N1BfVKoYtdk4hplDdGZTNyeWZZIaz2CZOSK9Ifz+\n1g0aKGpJR4rcRFmft/e7Eq8/RzIpAEHUGiZcKXIBSXKmFatQyBEMNHYtUZRA7OTg0VE2r+9e0Hcg\nk83j8dZ/L13XOHTkOT79zm0NbXQr+5nj8VTN3zfdhSw3y0pUFKVpNqK6Xnsl90KEQvYmoXJedz0s\nhsPZcqbdW76cZFmJ9nw4GR63LIt/+sUAmfEQlll7CMwXcKIy2kSwnG8HqiSdGi23rMWH0mgdeSId\nzQ3+mAvdyCHMCos3gkW4y1+Th7NuZNF1EU+NEQ/LsohGnGhBs0mls0QWyGUvhN/fzaFjcdatDuL1\nVA+FjIznFsybz8WBg8/z+mtW0NtRfypHUWRCofn7mWtlLivRkogHAr7JmdTT/cDrxfZ3CE4zTKl/\nneDmr1vLudTy1SyuaLeAJ54fZffzOYx87SdQWQVZav50bJg5hDnNMp1B13MUkhVRCUsgEzPQiifp\n6l3V1PjQSizLRNc0R8L8vrCBp4YT88T4MNGuYM2CDWBZaTweZ+xFNU0jFHTmxB4IRDk9lKUzUqAz\nOvtnPz0UI1xnCB5gPDaKSowbrnpB3d87FV7OOHoKLjFbxG3Tk0o/8MrJXAuJeMngJZdrdIPhFpwt\nFqblivaypBFj/0oEQaBownf+8yBasj7PcH/UmdOxaeqILRTt1EQMy5r9tCmmRUaKp+nq70VWmi+m\nK2oJR4rcREUjFJ5fVA2jyPCZIfwBD8FgfaF+n8+5N+NkKlE2UnECr8dPKqOTzcVYvWLqRF0oFJEa\n2CAahs7+gd18/G0X1mX5KwiUc9CJRHLRKn3tPvDp4lw5I1uW5UkRt/Piuq6XW7dKA0rqNUypuLtb\ncLaIuCftZUopRN6IZpdGfH7lh88wMezDMuo5cVp4fM2HWE1Lr3tYRz1ks2Po+epPGaMoMXpmlGhv\nGJ+/8UEnup5FMJ3xFo90BucNi6eSMRKjWQRBoXdlfdXflqXREW1+oEsJqYG+84WvKWNZUQ4dG+WC\nDfbm5cxIuu5CN4BDRw5wwxXdrOqpfTMlSSKhUBBd1xsOLztJNRH3+bwoilwuMBNFwS04O4dwc9rn\nKQv/Xkth39qfAJUjPsdiaX77zBBGrr5qXE9IdMRnXDeyLXImA9PUyMY1Fjo1WIbIxFCKYmeeSLS/\n7vtYloGhG46MI/WFbdeyuTBNg9HBs2g5BVDoWq3O29I1F4KQRRSdcT/LZNIE/M7lxisRBAGfr5sD\nR8YJBiASrr9aPJ6YQMsN8tpra5/gNdUelStXgLcblSJuDygJIggChmESDodqnsxVwi04Wxrc6vFl\nSr3FaLIs4ffbE42SyQxPPj9EJqHW3JNdolpvtoWBaRWwLA1JDC5cWV7nfeshFR+tPXpgCWTGdbTC\nSTp7ViCKtZ8gi8UkQovD4rlcmvHBCTDtjZLqM+nsrL/HOhh0LqqRy+eqbjCcwucNc/pMjP6+NKFQ\n7eFxyzJ5fv+z3PnGLcg1Grj4/V48nsbboxabKcMUjWw2V/741GQuD8FgANM0p+XEK0XcLThbOsw2\nMd5ZDFzRrqAeVzSfz4OqTh/x+dtnB9Gz9Z10BclCkmU0M4ZpFWyRJo8gFunv8rCyJ0jAI/P8sTOM\nxUVkIYwkhJDFIJU7ecPMtyw0ni8kKWbqfyMqpkVGcoMEOr2EwguLoq5nEazWhsXHRs6STwqAWv7a\nvrUddbcumWaOcMiZVjfTNPF5nTmxz8fwyDhebwexCY10dowVfbWduI8eP8w1F4bYtGrhSEDJ3lMQ\naLg9arGZLyIwczKXLEvIsozHY4/XvPPOOwkGg2zbdhnbt19JX5/zXRQuC2O1uSOak7iiXUEtoi1J\nIoGAF8MwSSYzWJZtAjEykWXfkTSWVmMlsWAh+7P4olk2ry+ycVWU7kiEjoBMX6ePzpCnXOxTyruN\nJzWeOzLOMwdHeO7QcfJFny3iYhjDyLesNzubSNHoU8U0RFKjRbLJE0R7OvF45hYnZ8PixqxTayo5\nQXI8hWVMD4GHe8RpQzlqRVGcmz6VTCUINFEDUAvZbLY8HU0UFbSizLHjQ6xb24soVt+QZTJpJsZP\n8JGbFw6Ll06rxaJGJpNb8OvbgXoNU0oiXqomv/32P2bHjqd59NFH+fKXv4TPF+AP//AdvOlNt7R6\n6S4VtIvF7WLginYFC4XHvV4Vj0chlytQLNp5MNO0ME2Tx/YMomdqOSVaSP4cvmiGl1/dyy2vuIKe\nziCpVKbqE68UivPJ8KILo7x4Ww+yLHFiOM2ew+PsGjjLgeN5VFY7ntPW9TxGwQHDl4LE+Ok43lCc\nSHc/0oyQeavC4ulUnMR4Ekv3wIyqekkx6e1fWfc9nO7NNhbBgjEWz+D1TLWTCYKALEc5emyUtWs6\nUNXZNRWWZbF3/7PccdPFrOjrnDc0fC7kr2dSMkxptKLdsmD16nWsXr2Bm256K5ZlcezY0RYNHnKZ\nD+scmAjnFMtKtBeK1FU7aYuiUJ4HnExmsSxr8kVu/21h8thzwxi5+U5LFpIvjyec4rqrerjpf1zC\nhtWdFIsa8Xiyrp/BfuPU6A3LvPLKfm68ZjVHzqb55r/t4+ywB5V+cMBZDSCXTeBcQY1APgWF7CCB\nDg/hSB8Aup5xLCwe7gwgCCLpdILEeAJLmy3WJbpW+Bqq2LasDB5P/cVcc6FpxYYd0GplbHx8mmBX\n4vFEOH0mQ1dnnsiMjcjpsyfYulJk8wo/sVi8an5XFEVkWSKRSJ8TJx5RFAiFghiGs4YpgiCwcWPj\ntq61Mj4+xje/eS+HDx/ivvu+A0ChUOAf/uFL9PT0curUSW699TbWrl3X8rW0C25Oe9kyW7RVVcHn\nU8nni+UBAaZpYVnm5NfD/uNxRoaFqu5nkjePGk7x4ss7ecOLr2DD6k48HpV0utEe0IoVTxpKrOn2\n8Bfv2s5/7TjLT397EFNfgUzzIddixsCpDUAJyxBJj2nkUieIdEVBEBEd2Bh4QwaGZnJm8CSWplJN\nrAEE0Zw1ZrRWfD7nTlKJVJKIg73ZMzEMHU2T5/WIVxQf8YROJjvKyhV2lKJQyHP61AB3vWfKRGV2\nfrdkH2pXSodCgaon8XahZJiSz+fLP0e9LHXB2Z49z/KSl1zHoUMHyx974IEf0NfXzzve8S6OHDnM\n5z//Ob72tfuWZH1LQbtP+XISV7QrqHyPEQQBv9+LKAqkUjlM05x2uhaEqS/+7z3D6NnZRWCCrKN2\nxLnmsgh/8NLtrO0LEQoFMAyzJUU6siTy6het5qoLu/nnXx1mz+EYKqsadkjLFxKYurOCXYlRkIgN\nDWFqAopPQvV58XjD00Zs1nQdU8M08hgJMDWT+cS6RLBTKs/JrgfTdLY3W5Zaazk7PDKOqi5cMCeK\nMoYR4uixQdat62XfwB5uedk6wv651ydJEqGQf1q1dT2V1kuBM4YpS+9wdv31N7Br145pH3viicd4\n3/v+JwCbNm3m8OFDdhthoHUzCNoJ8xzoUHAKV7QrsCwLURTLRimFgkYmY+fnbME2J0PoU9+Tzes8\nvS+GmZ8eLpV8WbpX5XjfH1zIJRs6yiMIFyPn1x3xcudbtrHr4Bjf+9VRUqkoCj3U+0aTz2Rw+pRd\niSBqaFkRyxIwihb5RA7IISomqk+0RdwXRpZtK1PDKKAVs2jFArqmYRQMDA1MXaBzdRTqMGSJdjZW\nrS2KOSzLTyabplDIkS/kJ//Okc/nKBTy6HqBYDBKd2cf3V29eL1zryuTTRPwt65qPJPNoCj15d4V\npYN9+4/SHchx7bbNc35NSfzS6WzZMhTmrrRuFxEPBHyoqkIikWqwhqC9Hc4mJmL4/VPPs0AgwMTE\nxPIRbTc8vjyxLKtcqZ1O58ov7tIpu/J0XeKp/aPkkx5KeV9BsFAiCV6wzcsfv/4KokHPZAuMUHUE\nYau4Yks3F6/v4GePneChJw8is6Zma1DLNNCzrX1zMowiljV7U2BqInkN8sk8kEeUTSxLwDJmhqXt\n9QW6FEShdsGWPSZ+f315ZMMoMj5xklTqDGMjAr0dfrqjPjavsv+OBoNEAjJhv4QqiRwfSrH7cIw9\nR44ymhLKAh6NdJZb0XK5HKrSut7siXi2ai67GqZpMB47xvtvm3uCVz3i1w4iXmpBA4jHU01O6Gpf\nh7OOjk6y2Wz5/5lMho6O1k3fazf++2cvbc9fTAtYdqJdrUJcliV8Pk+52Awoh8Mty6xaVf7Yc1Oh\ncVHR8HXFefMNa3j1i1bjnezlzOcLZLP5Fv1E8+NVJd768o1ce0kvX/nX/SQSXcgsnEPN5iYmQ4Et\nQsphpGs7xZt69c2DpIAv0FGPiR2RrtpD0pqWYyx2HIxRXnnVCl52+ZX4PNNfNqIooChKecMnCAKR\nSJCLN3bzpqLORCrPc0di7Dl6iCefTuIPdNLd2Uco2LpcdiqdrluwAcbGj/HKK3vo65ye7rHdwgJY\nltWw+C22iDvRgrbU+etaufbal7B37x62b7+cI0cOs3nzBcvmlL3cEOZ7YYyOps677L4kzRbtklFK\nPl8sn7JLrVxzna5LDI5n+bOv7qYw2o0cyLBiTYE/vfkiNq8OEwj4URSZVCrTNo5Q6ZzGvT/dz8Bx\nCZVVzHdqiI2cwSi0aE8nGBiFAqbR/BthdGUAWaonBGyx8ZJeFGX+6WH5Qorx2HG8UpzXXLOa39vW\nhyLXtt5SisX+Y1eAlcSoqGmcGS/y+HNneWTXCBvXX0pXZ18d66+NM4PDeGrIZVdSLGaJjT/NX//J\nlXiUqQ1VqXirUGjt5rMk4oqiIMtyUyJeGgHaTDqqXQX7mWd28uCDP+fJJ5/gppvexNvedisAX/3q\n/6Grq4szZ07zzne+u22qx3t6QsvmFLwYLGvRliQRv9+LaZpkswUkSSwbLVQLh1dy/38M8PBjWUS1\nyDUvCPHuG7cQngyHa5pOJpNtaPhIKzFMi3955CgPPRXHw3rmCrboepaJwSStCgVaQgY923yu3BOS\nCEXrsx/1hS3Wblxb9fPZ7ARjsWN0h/K89to1XLGlu66JVnNREnGvV0WW5XLF/4nBBPf/+37G0j42\nb9yGqjoxO9wOcY+MZusu6Dtxaie3/X4vV26dqs/welX8fh+pVBZNc85QphYaFXGfz4PX6yWVatRC\ntT0Kzs4XXNF2lmUr2h6Pitc73SjFsiActltYSuP6ikW9ah769GiGv//+Xl774lW84spVBAI+vF7P\nrAKdduTx54b51n8eQzLXz7I/TSaGKCRb9DoTC2gZk6Y3BIJF1+quuivj+9f7iERn91jn80kGRw6w\noQ9ee+0aLloXddQko5QLTiYzgFUOp8uyxMM7TvGdXxykp3czK/rWNX3fsfFxoL4Ct2RqhIh6nA+/\ndSqXHQz6kWV5chO79OYVtYi4vWapvPGuF/vtsDTswxVsJ3BF21mWnWgrikAgYJ9ostn8ZBh8eivX\n9BylAlh2aLOozdrhm5aFLEmEQna+L5XKLHlrSy2IoshQXOPz39lJOtWLjB1KtSyT8cGhOkeL1oaF\niannMLXmrx3q8+BROxf+wgpEyWTTJauntXpZlsVY7BiCfob3vG4LW9Y4a3QiiiKhkJ2vTaczc0Ze\nJEkkV7T4wX8dZtehLFs2X9bUxK/TZ0bwemtvS7Msg2PHH+cvbruE/k5f2XzENE1SqUzD62g1M0Vc\nEOyi0Uwm11BOfEqw27fg7FzEFW1nWXaiHYn40HV9TqOUakiSOK3QyN7h2yIuiiKBgI9sNl/2I253\nSi072Wye4bEUX/3xPo6f8aLQTz6fIDXaop9DyqKlmz+9yF6I9vRR70ko3C2wYvXq8v8LxQxnB/dy\n7cV+brl+Ix7V2Y1KKa+ay9Vu5LHv+ATf+eURPP6VrFuzpe5e8qJWJJEw550hPpORscO8aEuRN123\noaE1LzWlnHuxWMQ0zYZy4u2avz4fcEXbWZadaIui/Qfmb+WaD1mWUFUFr9eDIAjoujEZStfapuhs\nLgQBAgE75Fnpda7pJv/80GH++9kMuXEPWtb5AjTLMjH1/LyV4LUSXRVEbmCO9ZotEfz+MJZlEYuf\npJg7wXteewGXbHC+NaY0mtIuRKzPyEPTTf7j8ZP8etc4mzdtJxqpvcp8cHgERa79lF3UsoyP7uDu\nP7mCSNiP3+9twnxk8anWMw7zh9Mrv9YV7NbiirazLEvRtk/VZsNhbEWRCQYD5Wra0huDqsqIooSu\nT4XS28WL2T6NBCgW7QK5mViWxSPPDPKdnx8jN9qBqTss3GIBLdP800lSoKO/n3rDl4rXZOOF69C0\nHGcG93L5ZpW337AJv9fZn7OyL7jZVMmZ0Qxf+8kB/OENrFq5obbvGYzhUWtv9Tl9dg9vf3mUl1+9\nbjIXnGmL/HUt+P0+PB6FZDJdk2FKpYh/6EMf4sSJ42zffjkveMEVbN9+5bLqa15MXNF2lmUn2oJg\nTvZdWzSStyoVFKVS2TlPUIIgTBNxQRCm5cOX4g3R5/Pg83lrKpA7eCrBV360j9HTAYycM9XM4FzF\neLDHg9dbXy4boGuVjKQYZNNH+aNXb+SKLc4M/KikFa1RuYLOP/7bAYaSAS7YdNm8YzRT6RSFQu2F\neaapMXj2ce775PVYlkU6PXsz1444sTHSNJ2jR4+wY8dOnnlmJ3v2PMuVV76Qu+/+O6eXu+xxRdtZ\nlp1o26dsa9a/FyrYlSaLzXS9vlauqZ5dW8Ttdh+9HKZrZdGaKAoEgwEEwX5zq7WaNpYs8OUfPc+h\ngxbFZJDmi3IM9EIRy2z+tdu5pgOROjcTgo4SHmXrWpHbX7ulqp92M5RsalvRGmVaFj/97QkefS7F\nJRdeVbU1rN7e7Fj8FNdeWOAt1288Z+oxRNE2TNE0JwxTSlXioOs66XSaqIO+8rXw/e9/h8HBQaLR\nKKdOneQTn/g0Ho9zm+V2wBVtZ1mGoj0Ti5lCXnkKNwyD8fExLrxwiyOtXKWiNlWVkWUF0zSmibhT\nlOYb53IFcrn6T32abvLtBw/x6FNxCrFI1QlmNeFQAZoaEAh39tf1PZaYRA2O8M5X265wTs86FgQI\nBgNIktjy0PLT+0f5zq+Oc8HmKwmHpotzI73ZR088yWfetZW+jsYGyiw255thyvj4GLfeegs///l/\nIYoiH//4h3n5y1/Jq171mqVemqO4ou0sy87GdDZTu20ba/L0a3H27FnuvvsuVqzo5y/+4i8dGf9m\nGCaGUSifbOw8m4Lf70WW5cl8uC3ijRa1TfUEN2ouAYos8p7XbmF9/1m+94vjTeW5Tc2ZvZ8vXMcJ\nRDAw5WG2boI/fu3ldEWcP71IkkgoFETTdFKpxuYy18PVF9n2ol/98U46e7bS37um/LnYRBxZrr04\nr1DMsLobLtrUh65PbRrbtZDS67VTPM08p9tJsAG8Xi+KopDJZAiFQuRyOTZs2LjUy3Jpc9yTdhUe\nfPDnfPWrX+TWW9/FLbe8bdIVqxRKbywfXguKIqOqdnuZKIrldhVN0xYstrFFxB79mU5nHQu9HzgR\n5ys/OsD4GT9Gvk7xEzW0jANCIFh0r+6lln2mJWYRfYO8/fc38MqrV2HohuNpiFLV8mJMbZtJKqvx\ntZ/uI6V1sWn9RQiCyOmzI3g9tYd2h0cP8pqrJF5x5applquiKFRsHNujkLJZw5R2ntD14IM/51e/\n+gVdXd1YlsWHP/xn06Z1nQ+4J21ncUV7DgzD4K67Ps2tt97GBRdsqfhMY/nwRikVtZVEXBCEckGb\npmnT3sBKdpOtEpHxRJ4v/+s+Dh0ELRmg5k2LmEHLNF+A5uuQCAQXsiy1MOURVq0scMcbL2bjqmi5\n3ccwjPLj1mwaYspXvraq5VagGyY//PVRdhwusnnjpWSzEoJQ2+NsWRZHj/+We/70cgI+ZdrnKgsp\n7Y2jUNfG0UnsISXNmby0s2HKoUMD/NVffYb77/8esizzla98EUkSueOOO5d6aY7iirazuOHxOZAk\nic9+9u45PjM7lG7v4qf+7eQpvORRXcqjl4raVFUhEPBhmha6riNJIoIgNDEreGG6Il4+9c7tfPvB\nQ/x2xwTFifCC4XLLMjELzjwW3sD8pw9LyGOpZ3nNi3u56SUXo8jiZD6/lIaQUVUZv9+HLEsNpSEq\n3c0SieSS+srLksg7XrWZNX1D/ODXT7BqxRV4vbWFxzPZcS7dGJol2DDXc27KHdDn85S7IUqbn1Y9\n30qV+Pl8YzUZMHfBWTsxOjpKKBRGlu3XUVdXNyMjQ0u8Kpd2xz1pO8r8RW1OUwrRWpaFIIiTp8kp\nB6hWsedIjO/98jBnTkloqWD1qnAxj+aAC+b8vdkWphyjsyvBe99wYc02pHP11pe85ucKCZeKoNrR\n+e7ImSRf++kB/MEtRMIrFvz602f3cPuru7hsU/2tc/NNMHOqpdHjUQgE/E0VfrZb/nouDMPgS1+6\nB1VVCYVCHD16hA984CN0dzvfjriUuCdtZ3FFu6WU3sAqQ+nOiLjf78Xr9UxzryqdJhVFQZJKQtRc\nUVs1NN3kF0+e4t9/e4b0WAA955v1NRYZ9JwDvdm9Kl7PTFcwC1NKIihjvPTyTt768o2z5lzXylRI\neCqvWxkS9njUSXezxougWk0iU+RrP9nHeLqDvt6tVavkDVNj6Ozj3PM/r0ZqcnoZLCTiWt05aNtJ\nTq3ZMGUuzgXBXk64ou0srmgvKnOJeH1XKIVoFxpOIghMG3rSqtzkWDzPD359hKf2pKaHzAUDPVec\nHHHYHJ1rOhHL07ymxPr3Luvgdb+3lr7O2RuGZqgMCXs8dk93KWS8VAY5taAbJj98+CiP78uzdtV2\nJGl2P3osfooXrE9yy/WtqVK2WxqncuKWZU173lUTcUGAUCiAIAgkk406ybVvwdlyxhVtZ3FFe8mY\nXdS20Cl8qve6/mEOgiCUC9pmnoiKRa3p6uqpkLmIlgxiiXmHe7NtsWZSrF/fArGupNLdLJ8vTisI\nLAnRXFPflhq/38cTzw/zjZ8OsKJvOz7f9HTB0RNP8qlbN7GqO7Ao65k9bMealhO3LMtBw5T2LDhb\n7rii7SyuaLcN1fPh2WyWp576HTfd9AekUllH2nBEUawQ8dKb6VRYsxEdKoXMf/boaTIxBS2tYBSa\nexONrPAheQRQxrj20iivf/E6+lso1lDpbjb34Iy5hai2aVKtYqa15/FBe3qb6ttER9SebFYodnmq\nrwAAE4ZJREFUZjBzu/n0bZcv+vpKSJI0uQGSkWW5LNr5vG392shj1+4FZ8sdV7SdxRXttsUW8IGB\n/dx111/wwhe+kA9+8MO06k1p5kSkZoraxhJ5dh6MMXAywd5DMTIpET0ro+fkBUVckEwk1URUDSTF\nxBM2uOayDm566fqWi3XJ3UwUxUnb19rC4HM/ds673FVDkiTC4QCFgkY2O3VSTWc1vv5vBzg7EWBF\n30WMjB3mNVdJvPyKlS1fUy2UNkeFgoYkiZOTuIxp4fSFNNzNX7c/rmg7iyvabcxPfvIj7r//G3zw\ngx/lhhteOfnR1veHA9OKi6aK2qpXV5eYaetZ1HRODKU5cDLOgRMJBo4nyCQl9JyMqQtIyqRAqyb+\nIKzs8dHf5WdFp/33xhUhuqOt92IuCV+x2HiItsRUQaBcdrmzw+l63WM6F2K+0ZRgz4v/198e59Hd\nKTpC8Gdvu4jgHK1ei82UYcr0zVHJIbD02FVugHRdrxBxa7JewhXsdscVbWdxRbuNeeCBH/CSl/wP\nVq5cNeMzS2PyMruozRbx0pvu1PjP6sKnG2ZZxJMZjb4OH/1dPlZ0+YkGVce9wWuh1e5mlYVZlRug\nZm1DK+1qFyosjCULdIaX3mO8XsMUWZbL4fR4PM5HP/oxLr74Ii699HIuvXQ7Xu/55R52PuKKtrO4\non1esLj94ZXV1XZRm4VpWkiSuCS2ns1gn/gWz91sofayWtZgC1+pg8A5u9pWMxXGLzY0utSyLPbs\n2c3OnTt46qmnOHz4EFu2XMhtt72Hq6++pgUrdnECV7SdxRXt8xKLmULeKhG3C6D8SJKEYZjIsoRp\nmtOqq9sRu2K55NOeWTJ3M7uqf+okblvVTp3EZ+bVWzGzezEodT44Y5hiF5xls1mee243fX39rF+/\nwcHVLszJk8d56KFf4vF4ePbZXdx++3u5+OJti7qGcwVXtJ3FFe1lQWtMXqqFwyvzkopSmdN13uSl\nEUoC0o7uZpVmJaqqTOtzFkUBn681M7tbyZRhSqbhzod2KjgzDIOPf/zDfOELX0QURcbGxpAkiY6O\n2meZLydc0XYW13t8WVD5RjfbLx3qz4f7fPaoxLlOTrpuoOsGuUkdL4WCg0F/2TK0dApf7ClSfr+v\n7LjVDhuImZimSaFQLKcYSu1lfr8XURQxTRNVlREE2q5HfCZT1fgC8XiqCcOU9io4279/H5Zl8aMf\n/ZBCIU84HOENb7h5qZflskxwRXvZUW3oSW358FI4XBBE4vFUTW1RpZNiNjt9ilTlAIpWu41N5YEh\nHk+2tdhVYlkWHo+KrhukUkkkSUJVZbxeD8FgANM0poXT24WSYYqu6yQSjRrQt6fD2fDwIHv3Psdf\n/uXdBINB7rrr0yiKwo03vn6pl+ayDHBFe9kzW8RtQZst4vv27UUQ4MorryabbXRU4tQUqUymMhys\nlIefVIqQE+Iqy/awj3MtD1waUlLpgGcYBrmcMW16maLI+P3elreX1bvuZtIP08Ph7RVd9fsDrFu3\nnmAwCMBll23nmWd2uqLtsii4ou0yg5kibmIYJv/8z9/mRz96gL/+67vJZrM49UZaLRzs9aqOnCRL\nYfxq7mbtykKubCV03RbnmamIQMDnaHuZ0+uej3bKX8/FJZdsI5FIYBgGkiQxNDTEmjVrl3pZLssE\ntxDNZV7y+Tyf/ORHyeVyfPazf01vb+/kZxbH5KVU1Fayvax1DrYgCJM5dJFUKl33tKmlpJrxSL04\n0V5WD4GAH0WRSSbTDa+73QW7xKOPPsKuXU8TjXYwPDzEhz70MTye1psAnYu4hWjOsmxF++mnn+TR\nRx+ho6MDQRC4/fb3LvWS2pJkMsmvfvWf3HTTm5HlmYGZ+oeeNEvl4A5RFOcUISfdzRaTUhuarhuk\n01nHr18S8dLj51Q9QalewDStJtrn2q/gzMUZXNF2lmUp2vl8nne96w/57ncfQFVVPvWpj3HzzW/h\nqqteuNRLO8dZXJOXmSIEAqZpnpMmL07kgetl9izs2sZoVtKsYYpNexacuTiDK9rOsixz2nv37qG/\nfwWqas8bvvTS7TzxxGOuaDfN7Hz47NYy50S8sqgNIBTyI8sKuq4TCPjw+bxLPn2rFnw+L16vh2Qy\ns6jFY9XqCVTVzokvNL3MWcOU9is4c3FpR5alaE9MxPD7pzyLA4EgBw8OLOGKzlec7w+f8y7lsLLJ\nxESi/PGZ7VHNTC5rBZVTxRKJ5JLn3Q3DxDAK5ZP+fO1liiLj8agkEunzwjDFxeVcYVmKdkdH52QF\ntE0mk3bdjFpOtf7wqX83cgqfz91srvYoVZXx+ysrqxcuamsFkiQSCpX6mFOLeu9amf342UWBoVAA\nQRDQdQOPR0HThLo3Qa5gu7g0xrIU7W3bLmNoaJBisYiqqjz33G5uvvktS72sZUbt/eHVsN3NlJrd\nzUrtUZBHEChbrZZcu1pZWV1JaaNxruXdTdPC41EoFjXS6Ww5H17fJsgtOHNxaYZlWYgG8PTTv+OR\nR35NNNqBLMtu9XjbUX3oSSw2zokTx7juupeRSmUcyVXbgzsqJ5dRDqUXi5pj+XDbh9tDKtWeNqrV\nkGWZcLh6odx87WWDg4NEIlFEUXALzpYhbiGasyxb0XY517BPvrt27eBzn/sMt932bm666Y0tu5so\nitOmb00vytLqbmuy7V8DCAIkk85sNBYLr1fF7/fVZZhSEnFRFHjrW28hFotx+eVXcMUVV3PllS9k\n1arVSzI73WXxcUXbWVzRdjln+P73v8sPf/g9/vzPP8vVV5cq/RenP9zO59oiLstyXUVtkmT7cJ9r\nfeMAgYAPRVGaNkwZHh5h586d7Nz5FDt37uDFL34pH/vYJx1erUs74oq2s7iivUScOXOaf/zHr7F1\n64WMjIwQiUR497v/ZKmX1bZYlsW9936ZN73prfT19c/8LIvZHw5MCwVX2oUWi9Mnl52r+etSZACs\nyRREY9eZq+DMsiwMw5jDrKf1FAp53vve27j66mv4X//rgw1fxzRNPvnJj/L883t5//s/zKte9Wru\nvvuznDhxnM9+9m/o75/5HF2+uKLtLMuyEK0dSCYT3HDDq3jpS18GwK23voVrr30JF1540dIurE0R\nBIE77riz2mepXtTmfH84UHHCzk/L54ZCU0VtgiAgSWJTbVFLQSkyUChoZLONRgaqG6YIgrAkgg3w\nj/94LxdcsLXp64iiyF/+5d28+c2v4/LLrwBg9eo13HLL213BdmkpbjXIEnHRRZeUBRvsnbvP51u6\nBZ1XlIRCwt6XiliWhGUJWBYVbWbOUDJ5yWRyxONJEokUkiQiSVLZ4jMY9KOqStvncVVVIRIJkc3m\nGhZs+zEuna7b5y3mwQd/zmWXbWfFipWOXM/r9fLKV76Gn/3sxxiGwfHjx9i8+QJHru3iUo32eUUt\nYx599BFe+MJrWbdu/VIv5TylJB7S5J+5RNwZbFvPIMWizsREglgsUW5J83hUOjrCRKOhyVxxewW6\nfD4vgYCfZDJNoXB+OZwdO3aUEyeOc911L3f0ujff/Gb+/d9/ym9+8zDXXvtiR6/t4jIXbk57idm1\nawe//e0jfOADH0EU3T3U4uNcPtzjUQkEfAvaepZMShRFnixqq21yWSuxw/oiyWS64cr2djZM+fa3\n78c0TWRZYceOp9B1jeuuu55bbnl709f+4AfvYGxslG996/vldkGXKdyctrO011Z/mfH444+xe/cz\n3HnnRxkfH2NoaJBt2y5b6mUtM5zJhwcCPlRVIZFILWjMousGum7MmoFtjxKVJseP2pXprc6Fi6JA\nOBxE142mnNnaWbAB3vWu95T/XSwWyOVyjgg2wI03voHjx4+6gu2yKLiivUQcOLCfz3zmE2zdehHv\nf//7yOfzvPGNb3FFe8mpb+hJKpUkEPAhSQHi8VRDp9RSUVs2W2lSouDzeRAEoXwKb2Z85lzIskQo\nFCSXa2ay2Lk1oes3v/k1u3c/g6ZpPPTQg7zyla9u+Fpnzpxm1arVDAzs55Zb3ubgKl1cquOGx11c\namZ6GH3v3j185jN/zkc+8hFe/OL/0ZI7To3PVFBVebLobUrEGw1ll0L59RimzMS+dUmsl18E9Etf\nuod4fIJ169a77Zrz4IbHncUVbReXOrEsi5/97Mfcd9/X+dSnPs21176ExTJ5mRqfKSPLyrTJW7WK\nb8kwJZVKN+yxPhUOnxmZcHGZjivazuKGx11c6mRkZJhf/OI/+NrX7mPt2nUVn6l/6Em9zByfWSpq\n8/u9yLI8mQ+fu6htyjAFEonGQvnQ/vlrF5fzGfek7eKYS5TLTEqn2NaZvMxEUeTy4BNRFMv5csMw\nCAb9TRqmuILtUj/uSdtZ3JO2i2MuUS4zqRS22fPDAZz2Wqn0Qi8VtXm9HhTFh2VZiKKAx6OiaRqm\nWc+e/NwqOHNxOV9xRXuZU3KJOnz4ELncuTXM4txidmvZTBF3+hRuWRaSJCFJEolECtO0yifxQMA3\nY3JZ9aK2djVMcXFZjrhb5mVMq1yiXGqhdGKdcmqbcmkTHLFaDYUCk73jSXTdwDRNCoUiqVSGWCxB\nKpXBNE28Xg8dHREikRB+vxdJEikW7eEmrmC7uLQXbk57GdNKlyiXZrFm/Kk9Hy6KAqFQEMMwSKez\nNd9RlmVUVeY3v/kNn/rUJ9m27VIuv/xKrrrqRWzZciGSJDX0k7gsb9yctrO4ou0CwP33f4NcLucW\norUtcxW1zf6qkmFKPp8nl2vcMCWTyfLss7t56qmn2LnzKcbGxvjCF/43l132ggav6bJccUXbWVzR\nduE3v/k1P/7xv6BpGm9841uacolyWQymt5WV8uG/+tUv2bfveT72sT9r2DClWsHZxESMYDC06Fad\n7tz5cx9XtJ3FFW0Xl3McXde4994v8/jjj/G3f/v3rFmztqGitnZ0ONu//3nGxkanzZ3/8z+/y507\nfw7hirazuNXjLi7nOJ/73F+QTCb5xje+TTgcppGhJ+3qcHbRRZdM+787d95lueOKtkvbcPLkcR56\n6Jd4PB6efXYXt9/+Xi6+eNtSL6vtefvb38WmTZuR5dLLub6hJ+eKYYo7d97FxQ2Pu7QJhmHw8Y9/\nmC984YuIosjY2BiSJNHR0bHUSzvPmJkPh3PBMMWdO3/u4obHncU9abu0Bfv378OyLH70ox9SKOQJ\nhyO84Q03L/WyzkPaK/xdC+7ceReXKdwtq0tbMDw8yN69z3Hjja/nne98N7t3P8MvfvEfS70slyWm\nNHf++eef4/3vfx8f//hHOHnyxFIvy8VlyXBP2i5tgd8fYN269QSDQQAuu2w7zzyzkxtvfP0Sr8xl\nKbnwwot46KH/XupluLi0De5J26UmvvnNe7nuuhfx/e9/h+ef38sf/uHNfPvb9zt2/Usu2UYikcAw\n7HGSQ0NDrFmz1rHru7i4uJwPuIVoLjVz771fYXh4iDe84WYOHz7ELbe8zdHrP/roI+za9TTRaAfD\nw0N86EMfw+PxOnoPFxeXxcUtRHMWV7RdakbTNP74j99JV1cPf//3X0Zweq6ki4vLeYcr2s7ihsdd\nakZRFC666BKOHj3MxERsqZfj4uLisuxwT9ouNfPggz8nEAhw/Pgx9u7dwxe+8MWlXlJL+P73v8Pg\n4CDRaJRTp07yiU982g3Tu7g0iHvSdhb3pO1SEw888AO+9a1vEg5HWblyNb/73eN85jOfJJfLLfXS\nHGV8fIzvfvef+NCHPsZ73vM+8vkcjz76yFIvy8XFxQVwW75cauSWW942rfDsFa945RKupnV4vV4U\nRSGTyRAKhcjlcmzYsHGpl+Xi4uICuKLt4jKNQCDIHXd8gM985hN0dXXT09PLqlVrlnpZLi4uLoCb\n03ZxmcahQwP81V99hvvv/x6yLPOVr3wRSRK54447l3pp5xRPP/0kjz76CB0dHQiCwO23v3epl+Sy\nRLg5bWdxc9ouLhWMjo4SCoXLE7O6uropFotLvKpzi3w+zz33/A0f+MCHec973seRI4fYseOppV6W\ni8t5gSvaLi4VvOhF17Jhwya+8pUv8k//dB8HDuzj1lvfvdTLOqfYu3cP/f0rUFUVgEsv3c4TTzy2\nxKtycTk/cHPaLi4VSJLERz7yZ0u9jHOaiYkYfr+//P9AIMjBgwNLuCIXl/MH96Tt4uLiKB0dnWSz\n2fL/M5m0OxfdxcUhXNF2cXFxlG3bLmNoaLBcC/Dcc7u59tqXLPGqXFzOD9zqcReXNmN8fIxvfvNe\nDh8+xH33fQeAQqHAP/zDl+jp6eXUqZPceuttrF27bolXWp2nn/4djzzya6LRDmRZdqvHlzFu9biz\nuDltF5c2Y8+eZ3nJS67j0KGD5Y898MAP6Ovr5x3veBdHjhzm85//HF/72n1LuMr5ufrqa7j66muW\nehkuLucdbnjcxaXNuP76G6YVcgE88cRjbNt2GQCbNm3m8OFDZDLppViei4vLEjJveNzFxWVp2Lp1\n68uAewYGBq6a/P8A8NaBgYFnJ/9/GnjZwMDA4aVbpYuLy2LjnrRdXM4NRoBQxf/Dkx9zcXFZRrii\n7eJybvBz4FqArVu3XgrsHhgYSC7tklxcXBYbNzzu4tJmbN269Trgj4BXA/cCfz/5qXuAQWAzcPfA\nwMDBua/g4uJyvuKKtouLi4uLyzmCGx53cXFxcXE5R3BF28XFxcXF5Rzh/wf1yJcWwQN3KgAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1b1e0278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf1 = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "            cmap=mpl.cm.coolwarm, linewidth=0.5,\n",
    "            antialiased=True)\n",
    "surf2 = ax.plot_wireframe(X, Y, RZ, rstride=2, cstride=2,\n",
    "                          label='regression')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "ax.legend()\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: sin_plot_3d_2\n",
    "# title: Higher dimension regression\n",
    "# size: 60"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
